Asked by reporters about the men’s return, Mr. Trump replied, “The true honor is going to be if we have a victory in getting rid of nuclear weapons.”

The arrival of the men in Maryland capped a whirlwind journey for Mr. Pompeo, who secured their release during a 13-hour visit to North Korea to arrange the summit meeting.

The president spent the hours before their arrival in a celebratory mood. He mentioned in a cabinet meeting that “everyone thinks” he deserved the Nobel Peace Prize for overseeing the prisoners’ release.

“But I would never say it,” Mr. Trump continued. “The prize I want is victory for the world.”

The president had also posted excitedly on Twitter that he planned to greet the “Hostages (no longer)” upon their arrival. Their plane touched down just before 3 a.m.

In a statement as they traveled to the United States, the prisoners said that they wanted to give their “deep appreciation to the United States government, President Trump, Secretary Pompeo and the people of the United States for bringing us home.”

“We thank God and all our families and friends who prayed for us and for our return,” they said.

Mr. Trump, who delivered on a long-held promise this week by ending the United States’ involvement in the Iran nuclear deal, has sought to deliver on another by improving relations with North Korea after nearly seven decades of mutual antagonism.

Analysts are watching the negotiations closely to see if the return of the prisoners is a gesture of genuine good will from the North, or if Mr. Kim will ultimately use the release of the men as leverage for prolonging the time frame for reducing or completely dismantling North Korea’s nuclear abilities.