After more than an hour of discussion with Kim Yong Chol, Trump told reporters that denuclearization – and a formal end to the decades-old Korean war – would be on the table in Singapore, AFP reported.
But the US president warned he did not expect to immediately sign a deal to bring a halt to North Korea’s nuclear program.
"I never said it goes in one meeting. I think it's going to be a process, but the relationships are building and that's very positive," he said, after waving farewell to the North Korean leader's right-hand man.
The Korean War has been largely frozen since an armistice ended hostilities, but not the underlying conflict, in 1953. Since then, there have been occasional clashes on the divided peninsula.
"We talked about ending the war," Trump said.
"Historically it's very important, but we'll see. We did discuss that, the ending of the Korean War. Can you believe we're talking about the ending of the Korean War?"
Washington is determined that Kim should agree to what US officials call the "complete, verifiable and irreversible" end of North Korea's nuclear weapons and missile programs.
Kim says he is committed to "denuclearization" in some form, but he is expected to demand security guarantees in return.
Most expert observers are skeptical of a rapid breakthrough, and Trump admitted it would be a long and difficult process.
"We're not going to go in and sign something on June 12. We never were. I told him today, 'Take your time'," he said, adding nevertheless that he expects "a really positive result in the end."
Kim Yong Chol, the most senior North Korean to visit the United States in 18 years, spent almost 90 minutes in the Oval Office.
Afterward, Trump and US Secretary of State Mike Pompeo walked the North's delegation to their cars, smiling and shaking hands in front of the media before the motorcade pulled away.
Meanwhile, discussions between US and North Korean officials continued in Singapore and in the Demilitarized Zone dividing the Korean peninsula.
On Thursday, Kim Jong-un told Russia's Foreign Minister Sergei Lavrov that his commitment to denuclearization remains "unchanged and consistent and fixed," but experts warn he will seek concessions from Washington.
In addition to an end to the war, he is likely to want international recognition as well as guarantees against any strike by the US forces stationed in South Korea.
Secretary of Defense Jim Mattis, however, said Saturday that the presence of American troops in South Korea is not "on the table."
Seoul welcomed Trump's meeting with Kim Yong Chol.
"The delivery of a letter from Chairman Kim Jong-un to President Trump has apparently broadened and consolidated the road to the North Korea-US summit," said Kim Eui-gyeom, spokesman for South Korea's presidential Blue House.
China also welcomed the development, with Foreign Ministry spokeswoman Hua Chunying saying that Beijing hoped the two nations "will continue to move towards each other, to demonstrate sincerity, and to actively promote the preparations for the leaders' meeting."
Japanese premier Shinzo Abe meanwhile said, "I am determined to do my best so that it will be a historic summit."