WASHINGTON — President Donald Trump and Israeli Prime Minister Benjamin Netanyahu declined Wednesday to commit to the long-standing search for a two-state solution to the Israeli-Palestinian conflict, a shift favored by Israel’s right wing that could spark fresh turmoil in the region.

But Trump also appeared to catch Netanyahu off guard when he criticized the Israeli government’s recent sharp expansion of housing settlements in the occupied West Bank, land claimed by the Palestinians.

Appearing at a joint news conference before a White House summit, Trump turned to Netanyahu, who stood at the next lectern, and said, “I’d like to see you hold back on settlements for a little bit.”

Netanyahu countered that settlements could be discussed as part of a final peace deal, but added they were “not the core of the conflict.”

After years of chilly relations between Netanyahu and President Barack Obama, Netanyahu and Trump were all smiles, warm handshakes and gushing praise at their first get-together since the fall campaign.

That may have been the point for the nearly four-week-old presidency that appears in chaos, and for Netanyahu, who is battling allegations of corruption back home.

“For both sides, the primary objective of this meeting is to change the political theater of the relationship,” said Michelle Flournoy, a former defense official in the Clinton and Obama administrations. “To change the vibe, the feeling, the perception (to show) that ...you know, it’s all kumbaya.”

Trump and Netanyahu appeared in sync on most issues, especially on the elusive search for a long-term Mideast peace deal through a two-state solution.

For years, U.S. and Israeli leaders, as well as most of the international community, have advocated the vision of two nations, one Israeli and one Palestinian, living side-by-side, as the key to peace.

A day after an anonymous White House official told reporters that Trump was no longer committed to that approach, the president made it official.

Trump said he wanted to forge “a really great peace deal” and would support whatever solution Israelis and Palestinians wanted.

“I’m looking at two-state and one-state, and I like the one both parties like,” Trump said. “I can live with either one.”

Netanyahu, who has supported the two-state solution in the past, dodged the question when asked Wednesday.

Israel’s far right increasingly has pushed the idea of a single Israeli state of both Arabs and Jews, and control of the disputed West Bank, Golan Heights and other areas captured by Israel during the 1967 war.

Palestinians see much of that land as theirs, and insist on a separate sovereign state.

Other critics, including former Secretary of State John Kerry, note that Palestinians would soon outnumber Jews in a single-state scenario. They could use the ballot box to take control unless Israel abandons its democracy and restricts their rights the way South Africa once barred blacks from voting under apartheid.

Netanyahu defended Trump when asked about the xenophobic and anti-Semitic sentiments unleashed by some of his supporters during the presidential race last year.

“There is no greater friend of Israel,” Netanyahu said of Trump, then singled out the president’s son-in-law, Jared Kushner, as a lifelong, family friend.

Kushner, a 36-year-old observant Jew with no formal diplomatic experience, has been tapped by Trump to lead negotiations with Israel and the Palestinians.

But Palestinians will be suspicious of Kushner’s ties to Netanyahu, and as a newcomer, he may struggle with the complexities of the enduring conflict.

But Trump and Netanyahu said Saudi Arabia and other Arab states could be recruited to help negotiate a peace deal between Israel and the Palestinians.

Previous administrations have tried enlisting Arab states to craft a diplomatic solution, an approach known as “outside-in,” without evident success.

It stands in contrast to the “inside-out” strategy, which holds that resolving the conflict directly through the two-state solution would lead to peace in the broader Middle East.

Daniel Kurtzer, a former U.S. ambassador to Israel, was critical of Trump’s policy shift.

“If they think there’s a solution other than the two-state outcome, (then) they have not done their homework,” he told CNN.

Los Angeles Times’ special correspondent Joshua Mitnick contributed from Tel Aviv, Israel.

tracy.wilkinson@latimes.com