President Trump welcomed home three Americans freed by North Korea early Thursday in a flag-waving ceremony before dawn, calling their release a hopeful sign that North Korea will denuclearize.

“This is a special night for these three really great people,” Mr. Trump told reporters on the tarmac at Joint Base Andrews in Maryland shortly after 3 a.m. with the former detainees. “The true honor is going to be if we have a victory in getting rid of nuclear weapons.”

As he stood with the three men, Mr. Trump thanked North Korea’s Kim Jong-un for releasing the Americans, and said he believes Mr. Kim wants to reach an agreement on denuclearizing the Korean peninsula.

“We’re starting off on a new footing,” the president said. “I think he did this because I really think he wants to do something and bring that country into the real world. I really believe that.”

The president and Mr. Kim plan to meet soon at a historic summit to discuss North Korea giving up its nuclear weapons program. The date and location of the meeting will be announced within days, after Secretary of State Mike Pompeo nailed down more details in meetings in North Korea this week.

“Hopefully, everything is going to work out at the highest level,” Mr. Trump said. “We want to thank Kim Jong-un who really was excellent to these three incredible people.”

Asked by a reporter how it feels to be home, one of the men, Kim Dong-chul, said through a translator, “It’s like a dream. We are very, very happy.”

“We were treated in many different ways,” Mr. Kim said of his North Korean captors. “For me, I had to do a lot of labor. But when I got sick, I was also treated by them.”

When a reporter asked Mr. Trump whether the return of the three men is his proudest achievement, the president replied, “My proudest achievement will be — this is a part of it, but it will be when we denuclearize that entire peninsula. This is what people have been waiting for for a long time. Nobody thought we could be on this track in terms of the speed.”

First lady Melania Trump, Vice President Mike Pence and other senior administration officials joined Mr. Trump to celebrate the return of the Americans at the military base near Washington. The men, Kim Dong-chul, Kim Hak-song and Tony Kim, were released Wednesday amid a warming of relations between the longtime adversaries.

The president and first lady boarded the medical plane on which the men traveled to take a private moment with them, then appeared at the top of the airplane stairway with the three and applauded as the men held up their arms in what appeared to be gestures of triumph.

The freed prisoners appeared tired but in excellent spirits, flashing peace signs as they emerged from the aircraft. As the men entered into view, U.S. service members on the tarmac burst into applause and cheers.

After Mr. Trump’s remarks, the three men boarded a bus for Walter Reed National Military Medical Center. The White House said earlier they would be evaluated and receive medical treatment at the Washington-area facility before being reunited with their families.

Mr. Pompeo had secured their release in Pyongyang after meeting with Mr. Kim on final plans for the summit. The Americans had boarded Mr. Pompeo’s plane out of North Korea without assistance and then transferred in Japan to the Boeing C-40 outfitted with medical facilities for the trip back to the U.S.

During their flight back to the U.S., the State Department released a statement from the freed men.

“We would like to express our deep appreciation to the United States government, President Trump, Secretary Pompeo, and the people of the United States for bringing us home,” they said. “We thank God, and all our families and friends who prayed for us and for our return. God Bless America, the greatest nation in the world.”

Singapore has emerged as the likely host of the summit, late this month or in early June, as Mr. Trump seeks to negotiate denuclearization of the Korean peninsula in his highest-stakes foreign policy effort yet. Trump announced Wednesday that the demilitarized zone between the Koreas would not host the summit. Mr. Pompeo said the meeting would last one day and possibly a second.

Mr. Trump hailed Mr. Kim’s gesture as a sign of cooling tensions and growing opportunity on the Korean peninsula. Mr. Kim decided to grant amnesty to the three Americans at the “official suggestion” of the U.S. president, said North Korea’s official news agency, KCNA.

North Korea had accused the three Korean-Americans of anti-state activities. Their arrests were widely seen as politically motivated and had compounded the dire state of relations over the isolated nation’s nuclear weapons.

The president also noted that he and Mr. Pence this week had called the family of Otto Warmbier, the Ohio college student who died in June 2017 after being released from North Korean captivity. He had suffered brain injury of an undetermined cause.

“I want to pay my warmest respects to the parents of Otto Warmbier, who was a great young man who who really suffered,” Mr. Trump said. “His parents have become friends of ours. They are spectacular people, and I just want to pay my respects.”

Mr. Warmbier was arrested by North Korean authorities in January 2016, accused of stealing a propaganda poster and sentenced to 15 years in prison with hard labor. His parents, Fred and Cindy Warmbier, have filed a wrongful death lawsuit, accusing the government of torturing and killing their son.

“We are happy for the hostages and their families,” the Warmbiers said in a statement Wednesday. “We miss Otto.”

Mr. Trump praised Mr. Pompeo’s work and criticized The New York Times for a report this week that said the secretary of state was “AWOL” on the day that the president pulled the U.S. out of the Iranian nuclear deal. Mr. Pompeo was actually in North Korea on his mission to bring home the three Americans and complete the groundwork for the summit with Mr. Kim.

“I think our secretary of state, despite the fact that The New York Times said he was missing, he was in North Korea,” Mr. Trump said. “But I think our secretary of state has done a fantastic job.”

The president turned to Mr. Pompeo and asked, “Mike, did you know that you were missing? They couldn’t find him because he was in North Korea.”

Mr. Trump entered office as an emboldened North Korea developed new generations of nuclear weapons and ballistic missiles capable of hitting the continental U.S. Those advances were the subject of President Barack Obama’s starkest warning shortly before Mr. Trump took office, and this is a crisis he’s convinced his negotiating skills can resolve.

South Korea, Japan and others have credited Mr. Trump’s “maximum pressure” campaign of sanctions for Mr. Kim’s willingness to come to the negotiating table.

The release capped a dramatic day of diplomacy in Pyongyang. After Mr. Pompeo’s 90-minute meeting with Kim Jong-un, he gave reporters a fingers-crossed sign when asked about the prisoners as he returned to his hotel. It was only after a North Korean emissary arrived a bit later to inform him that the release was confirmed.

The three were the latest in a series of Americans who have been detained by North Korea in recent years for seemingly small offenses and typically freed when senior U.S. officials or statesmen personally visited to bail them out.

The highly public and politically tinged arrival ceremony for the former prisoners organized by the White House was in stark contrast to the low-key and very private reception that the State Department had envisioned and carried out from the moment they took custody of them.

Department officials took great pains on their release in North Korea, as well as on their flights to Japan and Alaska, to keep them sequestered not only from the two journalists traveling with Mr. Pompeo but also from staffers not immediately involved in their cases. The trio, along with medical personnel, including a psychiatrist, were cloistered in the middle of Mr. Pompeo’s plane in a small section of 12 business class-sized seats that was cordoned off by curtains on both ends.

State Department officials refused to discuss anything but the most basic details of their conditions, citing privacy concerns in keeping with the minimal amount of information they had released since the men were imprisoned.

Of the newly released detainees, Kim Dong-chul, a South Korean-born U.S. citizen, had been held the longest. The former Virginia resident was sentenced in April 2016 to 10 years in prison with hard labor after being convicted of espionage. He reportedly ran a trade and hotel service company in Rason, a special economic zone on North Korea’s border with Russia.

The other two detainees hadn’t been tried.

Kim Hak-song worked in agricultural development at an experimental farm run by the Pyongyang University of Science and Technology, or PUST. The university is the only privately funded college in North Korea and was founded in 2010 with donations from Christian groups. He was detained last May for alleged anti-state activities.

Tony Kim, who also uses the name Kim Sang-duk, was detained in April 2017 at the Pyongyang airport. He taught accounting at PUST. He was accused of committing unspecified criminal acts intended to overthrow the government.

On Capitol Hill, Senate Democratic leader Charles E. Schumer of New York celebrated the detainees’ return but warned that “we’ll see many more hostages” if the administration provides an incentive for imprisoning Americans.

“We are happy they’ve returned, but North Korea shouldn’t gain by taking Americans and then releasing them,” he said.

After the release of the detainees Thursday, North Korea’s state-run media explicitly mentioned plans for the summit for the first time Thursday. Pyongyang has been exceptionally cautious about its public framing of Kim Jong-un’s recent diplomatic moves, which are a major shift from the more aggressive focus on missile launches and nuclear development that heated tensions to a boil last year.

• This article is based in part on wire service reports.

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