Hanoi - North Korean leader Kim Jong Un was asked Thursday if he was ready to denuclearize and he responded through an interpreter: "If I was not ready, I wouldn't be here."
Kim's remark prompted Trump to add, "That might be the best answer you've ever heard."
When pressed during a late-morning media briefing if he was willing to take concrete steps to give up his nuclear weapons programme, Kim said: "That's what we are discussing right now."
The two leaders, meeting in Hanoi, also said they would be open to the idea of setting up a liaison office in each other's country, in a further sign of warming ties between the historical adversaries.
"That is something that is welcomeable," Kim said.
Trump said the idea of inching the countries toward more formal relations through an incremental step was "a great thing."
The president remained upbeat about his negotiations with Kim but cautioned those hoping for a quick resolution: "It doesn't mean we're doing it in one day, in one meeting."
"No matter what happens we'll ultimately have a deal that's really good for Chairman Kim and his country ... That's where it's all leading," Trump told reporters.
"We've had very, very productive discussions. The relationship is as good as it's ever been - I think better," Trump said.
Earlier Thursday, as the two leaders kicked off their second day of meetings, Trump said he was in "no rush" to make a deal over North Korean nuclear disarmament.
"Speed is not important to me. What is important is that we get the right deal ... I very much appreciate the non-testing," Trump said, referring to North Korea's pause in nuclear and intercontinental ballistic missile tests since 2017.
The president, who first met Kim in Singapore in June, becoming the first-ever sitting US president to meet a leader of North Korea, added that he had "great respect for Chairman Kim," saying, "When you have a good relationship a lot of good things happen."
Kim also expressed optimism about his negotiations with Trump, saying through an interpreter, "I hope that we can come to a great conclusion and I will do all my best to bring good results."
"We made a lot of efforts so far and we think now is time to come together in Hanoi and have this wonderful dialogue," Kim added, during a short press session at the Sofitel Legend Metropole Hanoi hotel, where the leaders also met the night before.
The US president reiterated that he thinks North Korea could be "an economic powerhouse" if the two sides reached an agreement over North Korea's nuclear weapons programme.
"With a little bit of help, I think it's going to be very special," Trump added.
The two leaders met privately on Wednesday evening for around half an hour in a closed-door session at the colonial-era Metropole before joining a small group of aides and interpreters for dinner.
In between those two events, the leaders offered each other praise, with Kim calling Trump "courageous" for initiating the talks and Trump hailing Kim as "my friend" and describing their relationship as "a good one."
In their talks on Thursday, Trump was expected to demand that Kim agree to allow inspectors into North Korea's various nuclear sites or to identify all of his country's nuclear facilities or to shut them down completely.
Kim was likely to press for sanctions relief or security assurances, including a diminished US military presence on the Korean Peninsula.
Both positions have been long entrenched, with each side thus far unwilling to make the first move.
On Wednesday, Trump repeatedly pointed to Vietnam - the hosting site for the current talks - as a model for North Korea, saying the South-East Asian country "is thriving like few places on earth" after opening up economically.
"North Korea would be the same, and very quickly, if it would denuclearize," Trump tweeted.
North Korea's economic potential is "like almost none other in history," the president added.
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## Editorial contacts - Reporting by: Bill Bredesen, Bennett Murray and Bac Pham in Hanoi - Editing by: Peter Godfrey, +61 2 9322 8065,
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