An invasion could also fuel unrest in neighboring countries and could be particularly destabilizing for governments already struggling to contain discontent over economic pain or political repression, such as Bahrain, Egypt and Jordan.
Iran has long backed Hamas, and Iran-backed regional militias hostile to Israel have threatened to open new fronts in the war, depending on Israel’s military response. Saudi Arabia is a potential target.
Since the war began, Saudi officials have returned to specific calls for a substantive Israeli-Palestinian peace process and for the creation of a Palestinian state with Jerusalem as its capital.
“If we are not willing to overcome all of the difficulties, all of the challenges, all of the history that is involved in this issue, then we will never have a real peace and security in the region,” Prince Faisal bin Farhan, the Saudi foreign minister, told reporters this week.
Despite the escalating violence, it appears that American and Saudi officials are holding on to hopes of a normalization deal with Israel.
Without that formal step, the limited ties that exist between the two countries — separated by a 22-mile drive through Jordan — have remained largely clandestine.
Senators said they left Riyadh with the impression that Saudi leaders would still like to recognize Israel when the right moment arrives.
American and Israeli officials often frame normalization as a way to help contain Iran.
Iran is Saudi Arabia’s most prominent regional rival. Prince Mohammed launched a disastrous Saudi-led military intervention in Yemen in 2015 aiming to oust the Iran-backed Houthi rebels who nonetheless remain firmly in power there.
But the crown prince, racing to diversify the kingdom’s oil-dependent economy, has recently pursued a less aggressive approach and sought to build bridges. Earlier this year, he re-established diplomatic ties with Iran. Mr. Blumenthal, however, said that a Saudi Arabia-Israel pact seemed unlikely before Israel “concludes its operation.”
During the call on Tuesday, Prince Mohammed and Mr. Biden “affirmed the importance of working toward a sustainable peace between Israelis and Palestinians as soon as the crisis subsides,” the White House said in its statement.
Prince Mohammed stressed the urgent need to halt military operations and return to a peace process to ensure that the Palestinians “obtain their legitimate rights,” the Saudi government said in its own statement. Neither statement mentioned a Palestinian state.
The potential deal that Saudi officials had been working on before the war included a path to a state for the Palestinians, the person with knowledge of the talks said.
Framing the prospect of building ties with Israel as a way to obtain greater rights for the Palestinians could allow Prince Mohammed to limit popular backlash in his own country, where hostility toward Israel and support for the Palestinians is widespread.
In response to questions about the Saudi warnings, the State Department said that “although U.S. diplomatic efforts are currently focused on the immediate crisis, we remain committed to the long-term goal of a more stable, prosperous and integrated Middle East region, including through normalization and advancement of a two-state solution.”
Before the Hamas attacks, however, American officials and analysts in Washington briefed on the talks said that the U.S.-Saudi discussions had been focused mainly on the Saudi security demands of the United States. Those officials and analysts said there had been no detailed discussion of the Palestinian issue.
An essay by Jake Sullivan, the U.S. national security adviser, posted on the Foreign Affairs site this week, said that American officials were “committed to a two-state solution.”
But editors had allowed Mr. Sullivan to rewrite an earlier version of the essay from before the Oct. 7 attacks. The original version, published in the print edition of the magazine, makes no mention of Palestinian nationhood. It merely said that, although tensions persisted between Israel and the Palestinians, the Biden administration had “de-escalated crises in Gaza.”