Trump's remarks come days after Secretary of State Mike Pompeo said "firm commitments" were made during a meeting between USA and North Korea officials at the Demilitarized Zone to discuss the repatriation of American service members' remains from the Korean War.
But the accord did not spell out a timetable for the process or say how it would be carried out.
He later added on Twitter Wednesday morning that "Russia has agreed to help with North Korea, where relationships with us are very good and the process is moving along". The president echoed his own statement to reporters from a day before, when he said that "we have no time limit [on denuclearization]". If the door's open in September, I will invite Kanye West with me to go to North Korea with me, ' Rodman told Us Weekly on Tuesday. "We have no speed limit". However, Pyongyang shouldn't look forward to an easing of sanctions any time soon, as, according to Trump, they will remain in place.
The president's latest comments on the timeline for denuclearisation appear to shift from his position ahead of the summit with Mr Kim, when he said denuclearisation should start "without delay". "We're just going through the process".
A senior USA defense official says Washington hopes North Korea returns about 50 sets of remains within two weeks, . but the details are still thought to be sketchy.
But since then, Mr Trump has suggested that dismantling North Korea's nuclear arsenal could be some way off.
North Korea will return to the United States in the coming weeks the remains of some of the American service members killed in the 1950-53 Korean War, Secretary of State Mike Pompeo said on Wednesday.