US Secretary of State Mike Pompeo said the United States hopes to achieve complete denuclearization of the Korean peninsula in two-and-a-half years, ABC News reported on Wednesday.
Trump also declared on social media on Wednesday that "there is no longer a nuclear threat from North Korea", after his meeting with Kim.
On Tuesday, following their historic Singapore meeting, Trump and Kim issued a joint statement that reaffirmed the North's commitment to "work toward complete denuclearization of the Korean Peninsula" and gave U.S. guarantees of security to North Korea.
The United States did, however, commit to suspending joint military exercises with South Korea, Trump told reporters before departing the summit site.
The video, which plays out in Korean and English, shows images of Trump and Kim smiling.
Mr Kim previously praised Mr Trump for taking the initiative with North Korea where previous presidents had not.
"So have a lot of other people", Trump said.
A government source familiar with the matter told Reuters that Japanese officials planned to discuss the summit meeting with North Korean officials at an global conference on Northeast Asian security to be held on Thursday and Friday in Ulaanbaatar, Mongolia. He said he won't disclose specific timelines but that the administration is hopeful that "major, major disarmament" steps can occur before the end of Trump's first term.
The military talks had been initially slated for May, but were postponed after the North called off another planned high-level meeting in protest against U.S.
Trump frequently salutes people he sees in a military uniform, and he saluted Singapore military officials while visiting there for the summit with Kim.
"We believe that Kim Jong Un understands the urgency. that we must do this quickly", he said of the effort to have North Korea abandon its nuclear weapons. Trump "could not have been more clear about his expectations with respect to North Korea's obligations for the return of the abductees", he added.
Speaking later in the day in Beijing, Pompeo said China, Japan and South Korea all acknowledged a corner had been turned on the Korean peninsula issue, but that all three had also acknowledged sanctions remained in place. -South Korea joint military exercises while North Korea proceeds with the denuclearization process.