Trump’s desire to cast himself as a global peacemaker has become one of the recurring themes of his second term, maybe a nod to a legacy.

Prime Minister Benjamin Netanyahu of Israel praised President Trump’s role in his country’s establishment of diplomatic relations with some Arab states. But Mr. Trump has supported Israeli actions that have strained those ties.

In a gesture of support, Netanyahu, during his latest visit to the White House on Monday, presented Trump with a copy of a letter he said he sent to the Nobel Prize committee. “It’s nominating you for the Peace Prize, which is well-deserved. And you should get it,” Netanyahu said.