“I think you will have a tremendous future with your country — a great leader,” Mr. Trump told Mr. Kim. “And I look forward to watching it happen and helping it to happen.” Here are the latest updates.

Go deeper: Mr. Trump has signaled that he is willing to shift his administration’s goals from immediate dismantlement of the North’s arsenal to limits on its size and reach. “I don’t want to rush anybody,” he said this past weekend. “As long as there is no testing, we’re happy.”

Another angle: In an interview with The Times, the highest-ranking North Korean diplomat to defect in years said Mr. Kim had no intention of relinquishing his nuclear arsenal.

House votes to block emergency declaration

The effort to prevent President Trump from diverting funding to a border wall without congressional approval is headed for a vote in the Senate in the coming weeks, after the House passed the measure on Tuesday.

Three Republican senators have already declared their backing for the measure, one shy of the number needed for Congress to ratify it. But it remains highly unlikely that there will be enough support to overturn Mr. Trump’s promised veto.