For the first time since Prime Minister Benjamin Netanyahu of Israel returned to office last December, he and President Biden met face to face on Wednesday in a session that both soothed and aggravated tensions between the leaders and demonstrated Mr. Biden’s wider commitment to Israeli security.

By ending his informal moratorium on in-person contact with Mr. Netanyahu, Mr. Biden showed he was prepared to overlook personal frustrations with the prime minister’s domestic policies in favor of furthering international projects of mutual U.S.-Israeli interest: blocking Iran from building a nuclear weapon and establishing formal relations for the first time between Israel and Saudi Arabia.

“Even when we have our differences, my commitment to Israel is ironclad,” Mr. Biden said at the start of the meeting at a hotel near the United Nations, pledging to ensure “that Iran never, never secures a nuclear weapon.”

Mr. Biden also hinted that Mr. Netanyahu might be invited to a more formal meeting at the White House within months — a major boost for the prime minister.

“I hope we will see each other in Washington by the end of the year,” the president said. Later, the White House issued a statement saying that Mr. Biden had extended a formal invitation.

But other comments by Mr. Biden, made before the meeting, made clear that the relationship remains thorny. He voiced measured criticism of Mr. Netanyahu’s efforts to reduce the power of Israel’s Supreme Court, which have set off one of the worst domestic crises in Israeli history.

Mr. Biden also pushed Mr. Netanyahu to preserve the possibility of creating a Palestinian state, implicitly criticizing several recent moves by Mr. Netanyahu’s government to entrench Israeli control of the West Bank.

“Today we’re going to discuss some of the hard issues: upholding democratic values that lie at the heart of our partnership, including checks and balances in our systems, and preserving the path to a negotiated two-state solution,” Mr. Biden said at the start of the meeting.

His comments reflected the deep unease in Washington over Mr. Netanyahu’s efforts to reduce the power of Israel’s judiciary.

U.S. officials are also unhappy about Mr. Netanyahu’s plans to build record numbers of Israeli homes and buildings in the Israeli-occupied West Bank, and to retroactively legalize unauthorized settlements built in the territory by Israeli civilians. Both actions will make it harder to create a Palestinian state, and also risk making Saudi Arabia warier of reaching a deal with Israel.

The meeting was private — and Mr. Biden and Mr. Netanyahu spent about 15 minutes alone, without aides — but U.S. and Israeli officials later said it focused on Iran’s nuclear enrichment program, which both men oppose but disagree on how to combat, and U.S.-led efforts to normalize relations between Israel and Saudi Arabia.

In the moments before the meeting began, Mr. Biden said to Mr. Netanyahu: “If you and I, 10 years ago, were talking about normalization with Saudi Arabia, I think we’d look at each other like, ‘Who’s been drinking what?’”

Like most Arab countries, Saudi Arabia has never recognized Israel, avoiding diplomatic ties out of solidarity with the Palestinians. But since late last year, the United States has been trying to broker a landmark normalization deal between the two countries, one that would see Saudi Arabia establishing relations with Israel in exchange for the United States’ supporting a civil nuclear program on Saudi soil and providing Riyadh with greater military support.

To secure the deal, Israel would need to make some concessions to the Palestinians, such as ceding them more land in the West Bank. But senior members of Mr. Netanyahu’s government — the most ultranationalist in Israeli history — are strongly opposed to such gestures, making it harder to forge a deal.

In an interview with Bret Baier of Fox News, excerpts of which were released on Wednesday, the Saudi crown prince, Mohammed bin Salman, made the kingdom’s concern clear. “For us, the Palestinian issue is very important,” he said. “We need to solve that part.”

Mr. Biden used the meeting to press the prime minister to do more to support the normalization process, White House officials said. A description of the meeting released by the White House after it was over said Mr. Biden had called on Mr. Netanyahu to “take immediate measures to improve the security and economic situation, maintain the viability of a two-state solution, and promote a just and lasting peace between Israelis and Palestinians.”

A senior Biden administration official, who spoke to reporters after the meeting on the condition of anonymity, said there was “a common understanding” among all the leaders in the region, including Mr. Netanyahu, that any normalization of relations with the Saudis would require dealing with the Palestinian issue.

The official said that during the meeting, there was a “basic meeting of the minds” about both the importance of the issue and also about the contours of what would be required.

But administration officials have said they recognize that Mr. Netanyahu operates within the constraints of his governing coalition, which includes ultranationalist members who oppose giving more sovereignty to the Palestinians. A senior Israeli official said that Mr. Netanyahu told Mr. Biden that the Palestinians should be included in the deal but not given the right to veto it.

The statement from the White House said that Mr. Biden had urged the prime minister and others to fulfill commitments — made to the Palestinian leadership at meetings brokered earlier this year by the United States — to de-escalate tensions in the Israeli-occupied West Bank. He also stressed to Mr. Netanyahu the need to refrain from “further unilateral measures,” a reference to building new settlements.

Though the two leaders have worked together for decades and describe each other as friends, Mr. Biden has called Mr. Netanyahu’s current coalition as “one of the most extremist” in Israeli history.

Back home, a photograph with the president may offer Mr. Netanyahu an opportunity to build a new narrative: to present himself as a statesman, remind Israelis of his extensive diplomatic experience, and suggest that the recent frictions with Mr. Biden have ebbed.

But Mr. Netanyahu’s critics, hundreds of whom protested outside the hotel, said the meeting should not distract from Mr. Netanyahu’s attempt to weaken the judiciary.

“You can have as many talks as you want and have all your slick interviews, but we don’t forget what you’re doing back in Israel,” said Inbal Biton, 48, an Israeli tech worker who joined the crowds of protesters outside the meeting.

In the meeting, Mr. Biden did not back away from his earlier criticism of the judicial overhaul. According to the White House description of the meeting, Mr. Biden “reiterated his concern about any fundamental changes to Israel’s democratic system, absent the broadest possible consensus.”

Mr. Netanyahu attempted to assuage Mr. Biden’s concerns about both his commitment to democracy and peace with the Palestinians.

“One thing is certain and will never change, and that is Israel’s commitment to democracy,” Mr. Netanyahu said before they met. “We will continue to hold the values that our two proud democracies hold dear.”

He also praised Mr. Biden’s efforts to mediate between Israel and Saudi Arabia. Successful talks, he said, would “bring an end to the Arab-Israeli conflict, bring about reconciliation between the Islamic world and the Jewish state and promote real peace between Israel and the Palestinians.”

Mr. Netanyahu’s message, however, was undermined by an earlier announcement by 11 lawmakers from his right-wing party, Likud. In a statement released on Wednesday, the lawmakers said they would block efforts to give land to the Palestinians in exchange for peace with Saudi Arabia.

But however unhappy the White House may be with the tactics of the Netanyahu coalition, the U.S.-Israel relationship, which has broad bipartisan support, appears as steady as ever.

U.S. officials see Israel as a key military partner in the Middle East, providing Israel with nearly $4 billion in military aid every year, and giving it strong diplomatic support at the United Nations Security Council.

“I don’t see anything material changing,” said Dov Zakheim, a former senior U.S. official who follows U.S.-Israeli relations. “We don’t just help the Israelis because we love them. We help Israel because it’s the most powerful military in the region.”

Gabby Sobelman contributed reporting from Rehovot, Israel.