In a first meeting, the United States and Iran show signs of pragmatism and limited aims, which would make success more likely. But hard-liners on both sides — and Israel — are bound to balk.

© Maansi Srivastava for The New York Times; Vahid Salemi/Associated Press

The Kremlin freed Marc Fogel, a teacher held for more than three years on drug charges, in a deal negotiated by Steve Witkoff, President Trump’s Middle East envoy.

The president turned up the pressure on the two nations to agree to his proposal for them to house the Palestinian population of Gaza and said the Palestinians would not have the right to return to the territory.

Although the president had been talking about the idea for weeks, there had been no meetings on the subject, and senior members of his government were taken by surprise.

The agreement removed one of the most vexing international conflicts that hovered over the start of his second term.

Pressure is on to reach a deal that would see Hamas release at least some hostages before President-elect Donald J. Trump takes office.