"Discussions are ongoing and they’re going very, very well," Trump told reporters.
"We have no time limit. We have no speed limit."
Trump said he discussed North Korea with Russian President Vladimir Putin on Monday at their summit in Helsinki.
"President Putin is going to be involved in the sense that he is with us," Trump said.
The Republican president met with Kim on June 12 for an unprecedented summit in Singapore during which the North Korean leader pledged to work toward denuclearisation of the peninsula.
But the accord did not spell out a timetable for the process or say how it would be carried out. Diplomats are now expected to hammer out the details.
More than a month later, no concrete progress has been reported and North Korea has complained the Americans are making unilateral demands.
Before the Singapore summit, the Trump administration said denuclearisation should start "without delay," and after the meeting, it spoke of the process beginning "very quickly."
A day after the meeting, US Secretary of State Mike Pompeo said the bulk of North Korea’s denuclearisation should be completed by the end of Trump’s term in 2020.
The White House has hailed the summit between Kim and Trump in Singapore as a major breakthrough toward disarming the nuclear-armed North in exchange for easing of sanctions and other help with economic development.
Pompeo met with Kim’s key aide this month during his latest trip to Pyongyang but as soon as he left, the North’s foreign ministry berated him over his "unilateral and gangster-like" demands.
Trump last week signaled optimism however, unveiling a letter from Kim in which the young leader hailed the "start of a meaningful journey" and tweeting "Great progress being made!" — AFP/VNS