JERUSALEM—President Biden warned that the U.S. wouldn’t “wait forever” for Iran to agree to revive the 2015 nuclear deal, and didn’t commit to raising the murder of journalist Jamal Khashoggi during a coming visit to Saudi Arabia.

Iran has emerged as a central theme of Mr. Biden’s ongoing trip to the Middle East as a result of rising concern over Tehran’s scaling up of its nuclear work, including producing uranium enriched to near weapons-grade material. Meanwhile, multilateral talks to revive the nuclear accord have stalled, in a setback for diplomatic efforts to roll back Iran’s nuclear program.

“We will not, let me say it again, we will not allow Iran to acquire a nuclear weapon,” Mr. Biden said Thursday during a news conference alongside Yair Lapid, Israel’s caretaker prime minister, on the second day of a four-day trip to the Middle East.

Mr. Biden said he remains committed to diplomacy with Iran. In an interview with Israeli media this week, the U.S. president said he would use force as a last resort to prevent Iran from acquiring a nuclear weapon.

Asked whether he would set a deadline for the negotiations, Mr. Biden said, “We’ve laid out for the leadership of Iran what we’re willing to accept in order to get back into the” nuclear agreement. “We’re waiting for their response. When that will come I’m not certain. But we’re not going to wait forever,” he said.

Mr. Lapid, who like other Israeli leaders has criticized the Iran nuclear deal, called on the U.S. to more aggressively threaten Tehran with a military response. “The only way to stop them is to put a credible military threat on the table,” he said.

Israel and Arab countries have been working more closely to counter Tehran. In turn, the U.S. has sought to encourage a deepening of regional alliances that could help contain Iran and allow Washington to focus on other regions, in particular China.

Stopping Iran developing a nuclear weapon has been a consistent position of previous U.S. administrations since Tehran revved up its nuclear work in the 1990s and early 2000s. U.S., Iranian and European officials met in Doha last month to try to revive the 2015 nuclear deal but failed to resolve differences on the conditions for doing so. There are no current plans for new negotiations, a senior European official said Thursday.

Mr. Biden heads to Saudi Arabia on Friday, a trip that has been criticized by members of his own party over the country’s human-rights record and for the 2018 killing of Mr. Khashoggi by Saudi agents. The U.S. intelligence community concluded that Crown Prince Mohammed bin Salman

ordered the killing of the Washington Post columnist. Riyadh denies the prince’s involvement in the killing.

Asked if he would confront Saudi leaders—including the crown prince—over the killing of Mr. Khashoggi, Mr. Biden didn’t directly answer.

“I always bring up human rights,” he said. “But my position on Khashoggi has been so clear. If anyone doesn’t understand it in Saudi Arabia or anywhere else then they haven’t been around too long.”

Earlier Thursday, Mr. Biden met with Mr. Lapid to discuss regional security and Iran, as his first presidential trip to the Middle East got under way.

Afterward, Mr. Biden said the two discussed the importance of integrating Israel into the region. Mr. Lapid said he was “trying to build even more moderate coalitions in the Middle East” and said he wanted to make sure there was no nuclear Iran.

Messrs. Biden and Lapid also signed a joint declaration underscoring the U.S.-Israel alliance and pledging never to allow Iran to acquire a nuclear weapon.

Ahead of the trip, the U.S. publicly highlighted intelligence that it says indicates Iran is preparing to provide Russia with drones for the battlefield in Ukraine, as well as training for its forces to use them. Officials said they hoped the development would galvanize countries in the region against Iran amid mounting concerns about Tehran’s advanced drone program, which the U.S. and its partners and allies in the region have blamed for some of the attacks in Saudi Arabia and other parts of the Middle East.

Israeli Defense Minister Benny Gantz,

in a meeting with President Biden on Wednesday, briefed the U.S. leader on the types of weapons Israel says Iran is spreading to allied militants in the region, including drones and guided missiles, according to a person familiar with the matter.

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Biden administration officials said the U.S. would take steps to work with Israel on the co-development of the Iron Beam, an experimental laser system envisioned as a shield against Iran-backed attacks. U.S. officials have been involved in discussions to form a regional air-defense partnership with Israel and other Arab nations designed to protect the countries against threats from Iran. Those talks have slowed amid concerns from some of the Arab nations involved in the discussions about the partnership, people familiar with the matter said.

Mr. Lapid declined to comment when asked Thursday about behind-the-scenes disagreements about the defense partnership. “We are working with everybody we can in order to promote regional security, especially facing the Iran regime,” he said.

There are security understandings between Israel and Arab countries in the region not yet party to the so-called Abraham Accords, a peace agreement between Israel and some Arab states, a person familiar with the matter said.

Iran says its nuclear work is entirely for peaceful purposes. It has warned its Arab neighbors against joining with Israel on defense matters, saying it would undermine regional security.

Mr. Biden also met on Thursday with Israeli President Isaac Herzog and with former prime minister, Benjamin Netanyahu, leader of the opposition. Besides Iran, topics of discussion with the Israeli leaders include the Israeli-Palestinian conflict and the war in Ukraine.

The U.S. president plans to underscore during his meetings with the Israeli officials that he supports a two-state solution to the conflict, but Biden administration officials said he didn’t plan to make new peace proposals during the trip. Mr. Biden said this week that he didn’t expect progress on a Palestinian state in the “near term.”

“Israel must remain an independent, democratic Jewish state,” Mr. Biden said on Thursday, calling Jerusalem the capital of Israel. “The best way to achieve that remains a two-state solution.”

Palestinians want East Jerusalem as the capital of their future state.

On Friday, Mr. Biden will meet with Palestinian Authority President Mahmoud Abbas, who is unhappy that the U.S. president hasn’t reversed the Trump administration’s approach to the Israeli-Palestinian conflict. The Biden administration has embraced the Abraham Accords, brokered under Mr. Trump, in which some Arab states recognized Israel without requiring any deal on the Palestinians.

Following the meeting with Mr. Abbas, the U.S. is planning to announce economic-related measures to aid Palestinians, including developing 4G in both the West Bank and Gaza, a senior Biden administration official said. Mr. Biden on Friday will also visit Augusta Victoria Hospital, where he is planning to announce U.S. funding for the East Jerusalem Hospital Network, U.S. officials said.

The visit is Mr. Biden’s 10th to Israel over his lengthy career in politics. The president emphasized his longstanding ties to the region, describing himself as a Zionist. On arrival Wednesday, Mr. Biden reunited with Mr. Netanyahu, who he has known for years, shaking his hand and greeting him warmly. White House officials said Mr. Biden was meeting with him to send the message that the U.S. relationship with Israel isn’t about just one leader and extends across the political spectrum.

Also on Thursday, Mr. Biden participated in a virtual summit with the leaders of Israel, India and the United Arab Emirates focused on food security and clean-energy development.

U.S. officials have so far declined to provide a detailed schedule for Mr. Biden’s visit to Saudi Arabia. The U.S. president will meet on Friday night with King Salman and Crown Prince Mohammed. On Saturday, he will attend a summit of Arab nations in Jeddah, the kingdom’s second-biggest city.

Mr. Biden had previously refused to deal with Prince Mohammed directly. But Russia’s war in Ukraine, which has exacerbated oil price increases, has reinforced the strategic importance of Saudi Arabia, with its heavy influence over global oil markets.

It remains to be seen whether Mr. Biden will be able to extract concessions from Saudi leaders on issues such as human rights and energy. Some of the president’s allies worry that without major progress on those issues, he could face backlash at home, where inflation is one of the top issues heading into the midterm elections.

“I think this trip is worthwhile, but only if we’re getting significant concessions from the Saudis: political prisoners and the war in Yemen,” said Sen. Chris Murphy (D., Conn.). “So I think it’s the president’s prerogative to meet with any world leader he sees fit, but the U.S.-Saudi relationship needs a pretty significant reboot.”

“We need a commitment from the Saudis that they are going to end this war [in Yemen] permanently,” Mr. Murphy said.

—Dov Lieber, Siobhan Hughes and Laurence Norman contributed to this article.

Corrections & Amplifications
Yair Lapid said, “There will be no nuclear Iran.” An earlier version of this article incorrectly attributed the quote to President Biden. Israel has reached security understandings with some Arab countries in the region not yet party to the Abraham Accords, a person familiar with the matter said. An earlier version of this article incorrectly said Israel has signed these agreements and they were shown to Mr. Biden. (Corrected on July 14)

Write to Andrew Restuccia at andrew.restuccia@wsj.com and Catherine Lucey at catherine.lucey@wsj.com