President Trump on Friday appeared optimistic about the prospects for peace in Gaza, saying it was “looking like we have a deal.” His administration is considering naming Tony Blair, the former British prime minister, to a role in overseeing Gaza after the fighting ends, according to three people familiar with the matter.

And on Thursday, Mr. Trump said he would not “allow” Israel to annex the West Bank.

But whether Mr. Trump can in fact bring the nearly two-year-old war to an end will probably depend on how much he is willing to push Prime Minister Benjamin Netanyahu of Israel, who has adamantly refused to back off his military campaign and has grown more defiant as multiple Western countries this week recognized a Palestinian state.

“It’s looking like we have a deal on Gaza,” Mr. Trump told reporters on Friday, adding: “I think it’s a deal that will get the hostages back. It’s going to be a deal that will end the war.”

He also said at the U.N. that he would not allow Israel to annex the West Bank. “There’s been enough. It’s time to stop now,” Mr. Trump said.

Ned Lazarus, an associate professor of international affairs at George Washington University’s Elliott School, said Mr. Trump’s statement about the West Bank, home to some three million Palestinians, was a significant pushback against the far right in Israel, which has agitated for the annexation of the territory.

Mr. Lazarus said that “Trump is probably the only one who can force Netanyahu off the course that he’s chosen.”