In a telephone conversation with South Korean President Moon Jae-in, the US president also asked Moon to "actively" help mediate future dialogue with the North Korean leader.
"While expressing disappointment over the failure to reach an agreement in the summit, President Trump reaffirmed his determination to resolve the issue through dialogue with North Korea in the future," Moon's presidential office Cheong Wa Dae said of the phone conversation.
The Trump-Kim meeting in Hanoi was cut short, although the US president said he and the North Korean leader both walked away in a good mood.
"Basically, they wanted the sanctions lifted in their entirety, but we couldn't do that," Trump told a press conference held earlier in the Vietnamese capital.
His call to the South Korean president was made from his Air Force One plane en route to the United States.
Cheong Wa Dae earlier expressed disappointment but said the US and North Korean leaders have already made more progress than ever.
Trump asked Moon to help mediate future dialogue with the North.
"In addition, (Trump) asked President Moon to actively perform the role of a mediator that may entail talking with Chairman Kim and letting him know the outcome of his dialogue," the Cheong Wa Dae spokesman said in a press release.
"President Trump suggested they work closely together so North Korea would actively implement its denuclearization commitment," he added. (Yonhap)