White said he would stay in the city for this week, and wants to see progress at the Trump-Kim Summit.
North Korean officials engaged in working-level talks for the summit briefed Kim after he arrived, the North's state news agency, KCNA, said on Wednesday.
In June past year in Singapore, the USA and North Korea released a four-point peace plan but there was little substance in the agreement.
"What he said was that the efforts that had been made in Singapore - this commitment that Chairman Kim made - have substantially taken down the risks to the American people".
"The main concern is whether the president, besieged by domestic distractions, will give away too much, and take a bad deal that leaves the United States less secure", said Victor Cha, a former White House official who took part in North Korea talks under previous Republican administrations.
In rare, revealing coverage of Kim's travel, while it is still going on, the North's Rodong Sinmun newspaper featured photographs of him getting a red-carpet send-off in Pyongyang and waving from a train carriage door while holding a cigarette. North Korea's long history of human rights abuses is also unlikely to be on the agenda.
Kim said Seoul welcomes any four-, three-, or two-way declaration to put an end to the war which mainly involved the two Koreas, the USA and China and that a two-way accord between the US and North Korea will technically suffice.
Some banners proclaiming the summit have gone up along Hanoi's tree-lined streets and some lamp posts are decked with North Korean, Vietnamese and US flags fluttering above a handshake design, but apart from that, for now at least, life goes on as normal.
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Anchor: South Korea says it would welcome the US and North Korea declaring a formal end to the Korean War during their upcoming summit later this week.
US Secretary of State Mike Pompeo says that after the upcoming summit, President Donald Trump may need to hold yet another bilateral summit on the North's denuclearization.
It is not known why North Korea's leader did not fly to his second summit with the USA president, but with a long journey ahead, he might soon invest in some wings similar to Air Force One.
He added sanctions should only be eased when full denuclearization seems in sight. "Maybe not", Trump said.
His former lawyer Michael Cohen is due to testify to Congress on February 28, and former Central Intelligence Agency analyst Soo Kim told AFP: "Trump could impulsively agree to give away significant concessions to Kim in Vietnam expressly for his own interests". Just this month Trump said: "South Korea - we defend them and lose a tremendous amount of money".
Meanwhile the respected USA -based website 38 North reported on Monday there is no indication Pyongyang is operating its nuclear reactors at the Yongbyon complex. "But the reason why we're engaged in this is because we believe there's a possibility that North Korea can make the choice to fully denuclearize".
North Korea state media on Sunday warned that Mr Trump's critics cold miss a historic opportunity to improve relations.