A view of the US-North Korea summit venue, Capella Hotel on Sentosa Island, Singapore June 4, 2018.
The Senate Democrats also called on North Korea to end production and enrichment of uranium and plutonium for military purposes, destroy test sites, eliminate ballistic missile programs, and submit to "robust compliance inspections".
"But it looks like it's coming along fine", Trump said at a White House event.
Last week, Trump met with a top North Korean official at the White House to plan for the summit.
Trump had already confirmed that would be a protracted effort in and of itself, given the size of North Korea's arsenal.
He also spent three weeks at Turning point in 2014 after returning from North Korea, where he organised an exhibition basketball game involving retired NBA players for North Korean leader Kim Jong-un. Trump said later that day that the Singapore meeting was back on.
Preparations are still underway for Kim and Trump's summit in Singapore, the first time a sitting US President will meet the leader of North Korea.
(ENGLISH) Edit No2247 6/5 "North Korea looks like it's moving along very well, a lot of - a lot of relationship being built; a lot of negotiation going on even before the trip".
US State Department spokeswoman Heather Nauert has denied the US would pay for North Korea in Singapore and said Washington was not asking anyone else to either.
His mentioning of a process several times could mean that he could accept phased denuclearisation as insisted on by the North Korean leader.
"We feel like things are continuing to move forward", Sanders said, "and good progress has been made, and we're continuing to prepare for the president's summit".
Stressing that Washington remains committed to completely verifiable and irreversible denuclearization of the Korean Peninsula, Nuaert said US talks with the DPRK in Panmunjom and Singapore "are ongoing".
"It's a sign he's comfortable shuffling people around", she said, adding that it's also a way to consolidate influence and avoid the formation of other power centers.
"Japan's economy does not stand out in northeast Asia as it did 16 years ago", he said, when Pyongyang and Tokyo last tried to negotiate a normalization of ties.