An argument is raging behind palace doors in Saudi Arabia: Now that the United Arab Emirates and Bahrain have forged ties with Israel, should the kingdom follow suit?

Saudi Arabia’s monarch, King Salman bin Abdulaziz, has been at odds with his son, Crown Prince Mohammed bin Salman, over embracing the Jewish state. The king is a longtime supporter of the Arab boycott of Israel and the Palestinians’ demand for an independent state. The prince wants to move past what he sees as an intractable conflict to join with Israel in business and align against Iran.

When President Trump announced on Aug. 13 that Israel and the U.A.E. were normalizing diplomatic ties, the deal stunned the 84-year-old king, who had just begun his summer holiday, according to people familiar with the matter, including Saudi advisers. His son wasn’t so surprised.

Prince Mohammed feared his father might block a deal that didn’t do enough to advance the cause of Palestinian statehood, those people said. If the king of Saudi Arabia, the biggest economy in the Middle East and the guardian of Islam’s holiest sites, didn’t support it, the neighboring Emiratis would be hard-pressed to move ahead. Prince Mohammed didn’t tell his father about the planned accord, which didn’t mention Palestinian statehood. Israel agreed only to suspend plans to annex parts of Israeli-occupied territory in the West Bank in return for diplomatic recognition from the U.A.E.

A furious King Salman later ordered his foreign minister to restate the kingdom’s commitment to the establishment of a Palestinian state, without mentioning the normalization deal. A royal family member close to him wrote an op-ed in a Saudi-owned newspaper reiterating that position and implying the Emiratis should have pressed the Israelis for more concessions.

“If any Arab state will follow the United Arab Emirates,” wrote Prince Turki al-Faisal, the former Saudi ambassador to the U.S., “it should demand in return a price, and it should be a high price.” The Saudi media ministry didn’t respond to a request to comment for this article.

Normalizing relations between Saudi Arabia and Israel before any deal for Palestinian statehood would be a seismic shift in the Middle East, upending a decades-old pan-Arab position. Tensions atop the Saudi ruling family suggest the kingdom’s position on the tumultuous region’s central conflict could change sooner than expected, but that such a shift would entail more turbulence.

The Trump administration has pressed to bring together Saudi Arabia and Israel, its top regional allies and Iran’s main rivals. Such an arrangement would allow for greater intelligence sharing and ease Israel’s isolation as Washington reduces its military presence in parts of the Middle East.

President Trump and Israeli Prime Minister Benjamin Netanyahu, left, at the White House on Tuesday, when the United Arab Emirates and Bahrain signed landmark agreements to recognize Israel.

President Trump and Israeli Prime Minister Benjamin Netanyahu, left, at the White House on Tuesday, when the United Arab Emirates and Bahrain signed landmark agreements to recognize Israel.

Photo: Doug Mills/Bloomberg News

“Israel has to wait it out,” said Yoel Guzansky, a former director of Iran and Gulf desk on Israel’s national security council. “It’s more a matter of when and not if. When and at what price, and the price [demanded by the Saudis] is being negotiated with the White House, not with Israel.”

Time is on Israel’s side. Saudi Arabia’s overwhelmingly young population feels less connected to the plight of the Palestinians than their parents and grandparents did, said David Rundell, a retired senior U.S. diplomat who worked in Saudi Arabia. Those “who grew up with two Arab-Israeli wars and the Palestinian cause beat into them since they were children are angry,” he said. “They feel the Emiratis have betrayed the Palestinians. Most Saudis under 30 don’t really care.”

Saudi Arabia and Israel have maintained discreet but frequent informal contacts on security issues, mostly related to Iran, for around 30 years. In recent years, Saudi Arabia has had to walk a fine line to pursue its twin goals of maintaining its alliance with the U.S., especially in confronting Iran, and continuing its longstanding support for Palestinians. That sometimes has led Saudi officials to voice one position in private and another in public, or even to take divergent public positions.

King Salman, a son of the modern Saudi state’s founder, lived through Israeli conquests of Arab territory, which instilled in him a devotion to the Palestinian cause, according to Saudi analysts and U.S. officials. When serving as governor of the Saudi capital before ascending the throne, he often referred to himself as “Palestine’s ambassador in Riyadh,” according to the actual Palestinian ambassador, Bassem Al Agha.

King Salman, right, with Palestinian President Mahmoud Abbas in Riyadh in 2017.

King Salman, right, with Palestinian President Mahmoud Abbas in Riyadh in 2017.

Photo: Al-Ekhbariya/Associated Press

In 1973, flush with petrodollars, Saudi Arabia imposed an oil embargo on the U.S., one of its closest allies, for supporting Israel in war against Egypt and Syria. It later forged a pan-Arab position that normal relations with Israel would come only with an independent Palestinian state.

Until the U.A.E. and Bahrain broke ranks this summer, that remained the stance of all Arab states, although Egypt and Jordan had already signed peace treaties with Israel.

For decades, King Salman has funneled billions of dollars to the Palestinians and developed personal relationships with most of their leaders.

When President Trump was entering office in 2017, King Salman sent him a message saying he believed in Israel’s right to exist but also in the Palestinians’ right to have their own state, said departing U.S. Ambassador Joseph Westphal, who relayed it to the president’s transition team. That May, during President Trump’s first trip abroad, Saudi Arabia allowed him to fly from Riyadh to Tel Aviv, a rare link between the two countries that underlined the aging monarch’s hope that the new U.S. administration would work toward his long-held goal of Palestinian statehood. He was soon disappointed.

When Jared Kushner, the president’s son-in-law and senior adviser, arrived in the region to sell President Trump’s Middle East peace plan to the Saudis, he promoted an early version that denied the Palestinians a capital in urban East Jerusalem and aligned with an Israeli push to grant the Palestinians limited self-government in patches of the West Bank, with no right of return for refugees displaced by earlier wars.

Prince Mohammed with White House senior adviser Jared Kushner in Saudi Arabia on Sept. 1.

Prince Mohammed with White House senior adviser Jared Kushner in Saudi Arabia on Sept. 1.

Photo: handout/Agence France-Presse/Getty Images

In a phone call with President Trump on Sept. 6, King Salman reiterated his desire for a solution to the Palestinian issue and referenced a 2002 Saudi-backed initiative promising normal relations with Israel only once that happens, according to a summary of the conversation from the Saudi state news agency.

By contrast, since assuming day-to-day responsibility of the Saudi government in 2017, the 35-year-old prince has expressed unusual openness toward Israel and accelerated engagements on security and commerce.

Soon after Prince Mohammed became heir apparent by replacing an older cousin in a late-night palace coup, he was privately pressuring Palestinian leaders to accept an early version of Mr. Trump’s peace plan, Arab officials familiar with the discussions have said. The Palestinians refused, saying it endangered their aspirations for statehood.

Prince Mohammed wants to move past what he sees as an intractable conflict to join with Israel in business and align against Iran.

Prince Mohammed wants to move past what he sees as an intractable conflict to join with Israel in business and align against Iran.

Photo: brendan smialowski/Agence France-Presse/Getty Images

In October 2017, the prince unveiled plans to build Neom, a $500 billion futuristic city-state across adjacent parts of Saudi Arabia, Jordan and Egypt—territory that abuts Israel. Prince Mohammed had suggested privately, according to his advisers and foreign diplomats, that he hoped the Israelis would play a big part in developing Neom, with potential investments in biotechnology and cybersecurity.

“He sees it as what’s practical and needed,” said Mr. Westphal, the U.S. ambassador to Saudi Arabia from 2014 to 2017, of the prince’s outreach to Israel. He said the king, who underwent gallbladder surgery in July and has been ailing for several years, “is not necessarily witting to everything that’s going on and involved to the extent that one would need to be involved to be in control of all these things.”

Prince Mohammed needs to maintain support from the Trump administration. The crown prince has faced international furor over the 2018 killing of dissident journalist Jamal Khashoggi by Saudi operatives. He denies ordering the murder but said he bears ultimate responsibility as the country’s de facto leader. The Saudi crown prince hasn’t visited the U.S. or Europe since Mr. Khashoggi’s murder.

Mr. Trump met with Prince Mohammed at the White House in 2018.

Mr. Trump met with Prince Mohammed at the White House in 2018.

Photo: mandel ngan/Agence France-Presse/Getty Images

With the Trump administration eager to recruit more Arab allies to replicate the U.A.E.-Israel agreement before the November elections, Mr. Kushner flew to Saudi Arabia to press the royal father-son duo. At a palace meeting on Sept. 1 in Neom, Prince Mohammed said the king wouldn’t accept the envoy’s proposal for a normalization deal between Saudi Arabia and Israel, according to people familiar with the discussion.

In light of his father’s resistance, Prince Mohammed told Mr. Kushner that the most the kingdom could do for now was to get tiny Bahrain to participate in a deal, those people said.

Asked if Saudi Arabia had given Bahrain approval to normalize ties with Israel, a spokesperson for the Bahrain government said it “remains committed to working with all of its strategic partners to achieve a just and enduring peace within the region.”

A senior Trump administration official said Prince Mohammed presented Saudi Arabia’s position about relations with Israel. In the meeting, the prince agreed to open Saudi airspace to flights to and from Israel and told Mr. Kushner that if Bahrain decides to normalize ties with Israel, “there was a clear pathway to do that,” the senior official said.

Bahrain’s leadership pushed ahead with joining the U.A.E. diplomatic deal. At the White House on Tuesday, Israeli Prime Minister Benjamin Netanyahu and the foreign ministers of the U.A.E. and Bahrain joined President Trump for a signing ceremony that the president called the foundation of a broader alignment against Iran. No Saudi representative attended.

From left, Bahrain Foreign Minister Abdullatif bin Rashid al-Zayani, Israeli Prime Minister Benjamin Netanyahu, President Trump, and UAE Foreign Minister Abdullah bin Zayed al Nahyan at the signing of the Abraham Accords on Tuesday.

From left, Bahrain Foreign Minister Abdullatif bin Rashid al-Zayani, Israeli Prime Minister Benjamin Netanyahu, President Trump, and UAE Foreign Minister Abdullah bin Zayed al Nahyan at the signing of the Abraham Accords on Tuesday.

Photo: saul loeb/Agence France-Presse/Getty Images

Under the so-called Abraham Accords, the former adversaries will establish embassies in one another’s countries and begin to cooperate economically, politically and socially. The Emiratis also reached a separate understanding that the U.S. would look favorably upon its requests for advanced F-35 stealth fighters.

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It won’t be easy for Saudi Arabia to erase one major obstacle to ties with Israel. Generations of Saudis have been conditioned to hate Jews. School textbooks called them swines and apes; mosque preachers have prayed for victory over the “invader and aggressor” Jews; and the news media has referred to Israel as “the Zionist enemy.”

Saudi Arabia’s Royal Family

Maintaining peace among the descendants of Abdulaziz ibn Saud has been critical for stability in the world’s top oil exporter

Prince Mohammed has pledged to root out religious extremism and promote a more tolerant vision of Islam that could accept other faiths, including Judaism. In 2018, he said he believes Israelis have a right to their own land—a break from the longstanding view of them as regional interlopers.

At the same time, the Saudi crown prince isn’t blind to the risks of rushing into a formal relationship with Israel, Saudi and Western political analysts said. It would expose the kingdom to criticism from regional adversaries for not only abandoning the Palestinians, but for allowing any arrangement that would see Israel maintain full control of Jerusalem and access to Al Aqsa Mosque, the third-holiest site in Islam.

Prince Mohammed is likely to push other states where Saudi Arabia enjoys influence, such as Sudan and Morocco, to normalize with Israel first, according to Mr. Rundell, the former U.S. diplomat who served in Saudi Arabia for 15 years. “If they do it before there’s a clear consensus among Arab states, they’ll make themselves a lightning rod” for criticism, he said.

Danny Danon, Israel’s ambassador to the United Nations from 2015 to 2020, said he had dozens of private conversations with Saudi and Emirati counterparts as well as visiting officials, largely to coordinate actions against Iran but also some social engagements. “In terms of having full recognition,” he said, “it will take more time.”

Although many anticipate Saudi Arabia will be the last Arab country to normalize ties with Israel, Prince Mohammed has a record of bucking expectations. Two advisers close to the crown prince said he wants to reach a deal with Israel but knows it is nearly impossible as long as the king is alive.

Meanwhile, he has directed local media to publish glowing coverage of the U.A.E. and Bahrain deals. A message to Saudi newspaper editors, seen by The Wall Street Journal, instructed them to defend the moves as “historical and honorable.”

Says a Saudi adviser familiar with the strategy: “He is testing the waters and preparing Saudis for what is coming next once he becomes king.”

Write to Stephen Kalin at stephen.kalin@wsj.com, Summer Said at summer.said@wsj.com and Felicia Schwartz at Felicia.Schwartz@wsj.com