A plane carrying three Americans released by North Korea landed at a military base bear Washington early on Thursday to be welcomed by U.S. President Donald Trump and his wife, Melania.
Welcoming the three Americans at a military base outside Washington, Mr Trump said of Mr Kim: "I really think he wants to do something."
He adds of the talks between his administration and the North Korean government: "It's never been taken this far."
Mr Trump said he will not disclose whether he will have any personal conversations with Mr Kim as they prepare for their historic summit in the coming weeks.
The US president was on hand to personally greet Kim Dong Chul, Kim Hak Song and Tony Kim at Joint Base Andrews, in the Washington area, along with many senior administration officials.
The men returned after US secretary of state Mike Pompeo was in Pyongyang to discuss Mr Trump's plans to meet Mr Kim.
The three former captives are being transported to Walter Reed National Military Medical Centre for further evaluation and medical treatment.
Despite a middle-of-the-night landing (2.42am local time, 7.42am BST), first lady Melania Trump, US vice president Mike Pence and a host of senior administration officials joined Mr Trump to celebrate the occasion.
The president and first lady boarded the medical plane on which the men travelled to take a private moment with them, then appeared at the top of the aeroplane stairway with the three and applauded as the men gestured in triumph.
Mr Trump said: "This is a special night for these three really great people."
On the US relationship with North Korea, Mr Trump said: "We're starting off on a new footing."
The released men's families were not on hand for the ceremony.
In a statement released through the US state department, the men said: "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.
"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 site for the Trump-Kim summit, late this month or in early June, as Mr Trump seeks to negotiate denuclearisation of the Korean peninsula in his highest-stakes foreign policy effort yet.
Mr Trump announced that the demilitarised zone between the Koreas would not host the summit. Mr Pompeo said the meeting would last one day and possibly a second.
The president had made a point of publicly thanking North Korea's leader for the prisoners' release - "I appreciate Kim Jong Un doing this" - and hailed it 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 US 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.