South Korea will work with the United States and North Korea to ensure they reach agreement on denuclearisation, the South's president says.

A second summit between US President Donald Trump and North Korean leader Kim Jong-unn, in Vietnam, was cut short after they failed to reach a deal on the extent of sanctions relief North Korea would get in exchange for steps to give up its nuclear program.

South Korea's President Moon Jae-in has been an active supporter of efforts to end confrontation on the Korean peninsula, meeting Kim three times last year and trying to facilitate his nuclear negotiations with the US.

"My administration will closely communicate and co-operate with the United States and North Korea so as to help their talks reach a complete settlement by any means," Moon said in a speech on Friday in the South Korean capital, Seoul.

The Hanoi summit came eight months after Trump and Kim met for the first time in Singapore and agreed to establish new relations and peace in exchange for a North Korean commitment to work towards complete denuclearisation of the Korean peninsula.

Trump said two days of talks had made good progress but it was important not to rush into a bad deal. He said he had walked away because of unacceptable North Korean demands.

"It was all about the sanctions," Trump told a news conference after the talks were cut short. "Basically, they wanted the sanctions lifted in their entirety, and we couldn't do that."

On Friday, Trump tweeted that the negotiations with Kim were "very substantive" and that "we know what they want and they know what we must have," but he gave no other details about any next steps. "Relationship very good, let's see what happens!" he wrote.

However, North Korean Foreign Minister Ri Yong Ho told a midnight news conference after Trump left Hanoi that North Korea had sought only a partial lifting of sanctions "related to people's livelihoods and unrelated to military sanctions".

He said North Korea had offered a realistic proposal involving the dismantling of all of its main nuclear site at Yongbyon, including plutonium and uranium facilities, by engineers from both countries.

"This is the biggest denuclearisation step we can take based on the current level of trust between the two countries," Ri said.

North Korean Vice Foreign Minister Choe Son Hui told the briefing she had the impression that Kim "might lose his willingness to pursue a deal" after the US side rejected a partial lifting of sanctions in return for destruction of Yongbyon, "something we had never offered before".

But despite the doubt that Choe raised, both sides have indicated they want to maintain the momentum and press on.

"We are anxious to get back to the table so we can continue that conversation that will ultimately lead to peace and stability, better life for the North Korean people, and a lower threat, a denuclearised North Korea," US Secretary of State Mike Pompeo told a news conference in Manila.

North Korean media adopted a conciliatory tone.

The state KCNA news agency said Kim and Trump had a constructive, sincere exchange and decided to continue productive talks, without mentioning that the talks ended abruptly with no agreement.

Kim, who is due to leave Vietnam on Saturday, also expressed gratitude to Trump for putting in efforts to get results, KCNA said.