WASHINGTON — President Trump said Wednesday that the United States would no longer insist on a Palestinian state as part of a peace accord between Israel and the Palestinians, backing away from a policy that has underpinned the US role in Middle East peace efforts since the Clinton administration.

“I’m looking at two-state and one-state’’ formulations, Trump said, appearing in a joint news conference at the White House with Prime Minister Benjamin Netanyahu of Israel. “I like the one that both parties like. I’m very happy with the one that both parties like. I can live with either one.’’

Trump’s comments were a striking departure from two decades of diplomatic orthodoxy, and they raised a host of thorny questions about the viability of his position. The Palestinians are highly unlikely to accept anything short of a sovereign state, and a single Israeli state encompassing the Palestinians would either become undemocratic or no longer Jewish, given the faster growth rate of the Arab population.

Trump did not address these dynamics, preferring to focus on his confidence that he could produce a breakthrough agreement.

“I think we’re going to make a deal,’’ Trump said, describing that as personally important to him. “It might be a better and better deal than people in this room even understand.’’

But even as Trump drastically reoriented US policy, he told Netanyahu to stop building new housing in the West Bank for the moment.

“I’d like to see you hold back on settlements for a little bit,’’ he told Netanyahu, whose government has been racing to announce new settlement construction in the weeks since Trump’s inauguration.

The president also stressed that Israel would have to be flexible in any future peace talks.

“As with any successful negotiation, both sides will have to make compromises,’’ Trump said.

Turning to Netanyahu, he asked, “You know that, right?’’

Netanyahu responded with a smile. “Both sides,’’ he said, emphasizing the first word.

Nonetheless, Netanyahu, who nominally supports a two-state solution, embraced Trump’s declaration, saying he preferred to deal with “substance’’ rather than “labels’’ in negotiating.

He noted that the concept of the two-state solution meant different things to different people in the region. And he repeated his two prerequisites — that the Palestinians recognize Israel as a Jewish state and that Israel maintain security control over the entire West Bank. The obstacle to peace, he said, is Palestinian hate, as demonstrated by building statues to those who carry out terrorist attacks and paying their families salaries. “This is the source of the conflict,’’ he said.

Trump and Jared Kushner, his son-in-law and senior adviser, have been exploring an approach called the outside-in strategy, enlisting Arab states in the region that already have found common cause with Israel against their mutual enemy Iran to help broker a settlement with the Palestinians. But it is not at all clear Palestinians would accept an arrangement that did not leave them with a state of their own.

Until now, Trump’s team has largely avoided conversations with Palestinian leaders. But Mike Pompeo, the CIA director, met with Mahmoud Abbas, the Palestinian Authority president, in Ramallah in the West Bank on Tuesday, according to the Associated Press.

The idea of an independent Palestinian state comprising the West Bank and Gaza became the central theme of Middle East peace efforts in the 1990s after the Oslo accords were signed. Bill Clinton was the first president to endorse a two-state solution, saying in a speech in January 2001, just two weeks before leaving office, that the conflict would never be settled without “a sovereign, viable Palestinian state.’’

His successor, George W. Bush, picked that up, becoming the first president to make it official US policy. Barack Obama considered a two-state solution the bedrock of Washington’s approach to the region.

But momentum for the idea of side-by-side states has ebbed not just in Washington but in the region, where many Israelis and Palestinians have given up hope or changed their minds about the concept.

Netanyahu arrived at a tumultuous time at the White House, just two days after Trump forced out his national security adviser, Michael Flynn, for withholding the truth about a conversation with Russia’s ambassador.

Netanyahu lost probably his most important ally against Iran with Flynn’s departure. During last year’s campaign, Trump repeatedly criticized Obama’s nuclear agreement with Iran as a terrible deal, but his administration has indicated that it does not intend to rip it up, at least not immediately, even as it imposes new sanctions on Tehran over its recent ballistic missile tests.

At the news conference, Trump again called the agreement “one of the worst deals I’ve ever seen’’ but said nothing about abandoning it or even renegotiating it. Instead, he simply vowed to keep Iran from becoming a nuclear power.

“I will do more to prevent Iran from ever developing — I mean ever — a nuclear weapon,’’ he said.

Netanyahu wants to ensure that if the deal is not scrapped, it is enforced rigorously, a goal with much sympathy in the White House.