Asked whether he was confident about the prospects for a deal, Kim replied: "Well, it's too early to tell, but I wouldn't say that I'm pessimistic".
Mr Trump, responding to that, said: "That might be the best answer you've ever heard".
Kim Yo Jong was seen standing close by, watching on from the sidelines as the two world leaders greeted each other in Hanoi.
He then added that he hopes that they will be successful with time and that he will really try to make that happen.
Asked by a reporter if he was "walking back" on denuclearization demands, Trump said "no".
The leaders are in Hanoi for their second summit following a historic first meeting in Singapore last June that produced little more than a vaguely worded agreement to "work toward complete denuclearisation of the Korean peninsula".
Looking relaxed but appearing to say little, they indulged in a poolside stroll Thursday around the gardens of the luxury Metropole Hotel, a Colonial-era building that has played hosts to stars ranging from Charlie Chaplin to Brad Pitt.
"What's important is that we do the right deal", said President Trump.
Trump has once again asserted that he was in "no rush" to make an agreement - following an early report by NBC that the USA was prepared to back away from a demand that North Korea provide a full accounting of its nuclear weapons programs.
Director of National Intelligence Dan Coats told a congressional panel last month that North Korea "has halted its provocative behavior" by refraining from missile tests and nuclear tests for more than a year.
Released Indian Pilot Says He Suffered 'Mental Harassment' in Pakistan
The developments came a day after India conducted airstrikes against alleged militant positions in Pakistani-controlled Kashmir. According to the Indian Air Force , in the same clash another MiG-21 shot down Pakistan's F-16 of United States manufacture.
Well, I want to just say it's an honor to be with Chairman Kim. "I feel good results will come out".
"There must be people who watch us having a wonderful time, like a scene from a fantasy movie".
Speaking ahead of their talks, Mr Trump appeared to again address scepticism about the success and progress of their last summit, saying he wanted to get the "right deal".
"But we couldn't do that", the president said.
After a "joint agreement signing ceremony" Trump plans a news conference at 3:50 p.m. Hanoi time (0850 GMT).
It is not clear what the joint agreement will include.
The US side had been hoping for major progress in dismantling equipment and facilities at the main North Korean nuclear complex at Yongbyon.
US intelligence officials have said there is no sign North Korea would eve give up its entire arsenal of nuclear weapons, which Kim's ruling family sees as vital to its survival.
"For his part, Trump said the idea was a "great thing".
U.S. Secretary of State Mike Pompeo, in a phone call with China's top diplomat Yang Jiechi on Friday, reiterated Washington's support for keeping in place United Nations sanctions on North Korea, saying they "remain a central pillar" of efforts to pressure Pyongyang to denuclearize, the U.S. State Department said in a statement.
Trump's statement could mean any US efforts to dismantle Pyongyang's program, including the core nuclear program at Yongbyon, could be postponed.