Senate Majority Leader Mitch McConnell said that Trump "should be commended for his personal commitment to persuading Kim Jong Un to pursue a different path - and for walking away when it became clear North Korea was not ready to commit enough to denuclearisation".
Trump indicated a more flexible stance in the run-up to Hanoi, saying he was in no rush on denuclearization as long as North Korea, which has not tested a nuclear weapon or intercontinental ballistic missile since 2017, maintained that freeze.
"Speed's not that important to me", he said as he began talks with Mr Kim at the Sofitel Legend Metropole hotel on Wednesday.
It is unclear if a "joint agreement signing ceremony" will still be held and Mr Trump has brought forward a news conference, which is now scheduled for 14:00 local time (07:00 GMT).
Already, some intrigue has swirled around the first talks between the two leaders.
PRESIDENT TRUMP: Thank you very much.
He added: "Chairman Kim if you're smart, you'll take the way out given to you by President Trump if you're actually trying to play the guy, you're gonna regret this effort".
Trump predicted longterm "fantastic success" when it comes to North Korea, saying the country will be "an economic powerhouse".
To this end, Kim arrived in Vietnam after a 66-hour long train journey which would only take six hours by air.More news: Japanese PM Abe says fully backs Trump over North Korea no deal
Trump said Cohen "lied a lot" during Congressional testimony in Washington on Wednesday, though he had told the truth when he said there had been "no collusion" with Russian Federation.
But there has been little progress since.
When asked by a member of the White House press pool about his outlook on the summit on Thursday, Kim said: "It's too early to say".
USA concessions could include opening liaison offices or clearing the way for inter-Korean projects, but critics say Trump risks squandering vital leverage if he gives away too much, too quickly. "No rush. We just want to do the right deal".
"He speaks, and people sit up at attention", Trump said past year.
Moon has been active in efforts to end confrontation on the Korean peninsula, meeting Kim three times a year ago and trying to facilitate his nuclear negotiations with the United States. Even Trump's director of national intelligence, Dan Coats, said he didn't know.
"We came all the way to Hanoi to meet again, 261 days later", he told the United States president, vowing to do his best to ensure a "great outcome" from the talks.
Sure Mark. The two leaders seem to have got along well in their first meeting in Hanoi last night seeing from President Trump's tweets and North Korea's state-run news agency's report. But before they disappeared to square off, Kim did something apparently unprecedented: he answered a journalist's questions.
"I believe that starting from yesterday, the whole world is looking at this spot right now", Kim said via his translator.
Trump said he and Kim had discussed dismantling North Korea's main nuclear facility at Yongbyon, which Kim was willing to do, but he had wanted sanctions relief.