Donald Trump has said he is considering a potential third nuclear summit with North Korea’s leader Kim Jong-un.

“We will be discussing that and potential meetings, further meetings with North Korea and Kim Jong-un,” Trump said in the Oval Office at the start of talks with South Korean President Moon Jae-in.

A third summit would follow on Trump’s historic breakthrough last year, when he met Kim in Singapore, and a follow-up this February in Hanoi that ended without progress in getting North Korea to give up nuclear weapons.

Trumps’s announcement came as North Korea replaced its long-serving nominal head of state with a close aide to leader Kim Jong-un who was placed on a US sanctions list last year for alleged human rights abuses.

Kim Yong Nam, who held the position for almost 20 years, was replaced by Choe Ryong Hae, who will take over the role of representing Pyongyang at international engagements, the state news agency KCNA said.

Both Trump and Moon are heavily invested in bringing North Korea out of the cold. But the unsuccessful summit in Vietnam was a setback for the two allies that has yet to be resolved.

At the White House, the US president insisted that a peaceful resolution of the North Korea standoff remains within reach, and that he continues to place considerable hope in his personal brand of diplomacy.

“I enjoy the summits, I enjoy being with the chairman,” he said.

Kim is “a person I’ve gotten to know very well, and respect and hopefully, and I really believe over a period of time, a lot of tremendous things will happen. I think North Korea has a tremendous potential,” Trump said.

The Vietnam summit ended without Trump being able to extract major concessions from Kim on the country’s nuclear arsenal or Kim getting the reduction he wanted in heavy economic sanctions brought to pressure him into cooperating.

Despite the sanctions, Trump said on Thursday that he supports unspecified South Korean moves to bring humanitarian relief.

“We are discussing certain humanitarian things right now. I’m OK with that, to be honest,” he said.

Although the broader sanctions should “remain in place,” he said he opposes any further tightening and noted that he had stopped planned new measures.

There was “the option of significantly increasing them …, but I didn’t want to do that,” he said.

Trump continues to face criticism that he is out of his depth in talks with Kim, and that sitting down with the dictator has yet to bring much benefit.

Moon has staked his presidency on engagement with isolated North Korea, pushing for a resumption of South Korean tourism to the North’s Mount Kumgang and operations at the Kaesong Industrial Complex, where companies from the South used to be staffed by workers from the North.

But Moon’s plan to unveil details of such projects on 1 March, right after the Hanoi summit, was scrapped and he is under pressure from opponents on the right. One lawmaker branded him the North Korean’s “top spokesman.”

Kim himself has used the impasse to speak out against international sanctions and warn in colourful, defiant terms that his country will not bow to pressure.

Shortly after the Hanoi summit, a series of satellite images emerged suggesting increased activity at the North’s Sohae rocket site, triggering international alarm that the nuclear-armed state might be preparing a long-range or space launch.