US President Donald Trump received a “very positive” letter from North Korean leader Kim Jong-un seeking a follow-up meeting after their historic summit in Singapore, the White House said.

US President Donald Trump received a “very warm, very positive” letter from North Korean leader Kim Jong-un asking for a second meeting and the White House was looking at scheduling one, White House spokeswoman Sarah Sanders said on Monday.

The two countries have been discussing North Korea’s nuclear programmes since their leaders met in Singapore in June, although that summit’s outcome was criticised for being short on concrete details about how and whether Kim was willing to give up weapons that threaten the United States.

The likely timing of a second Trump-Kim meeting was unclear.

South Korea’s President Moon Jae-in called for a “bold decision” by Trump and Kim on denuclearisation.

“The complete denuclearisation of the Korean peninsula is an issue that should fundamentally be resolved between the US and North Korea through negotiation,” Moon told a cabinet meeting.

“But until talks and communication between the North and the US become more active, we cannot but work to mediate between them,” he said, adding, “President Trump and Chairman Kim have asked that I play this role.”

Moon is scheduled to have his third summit with Kim next week in Pyongyang, and his government had pushed for a three-way summit involving Trump, with the aim of agreeing a joint declaration to end the 1950-53 Korean War.

The conflict ended with an armistice, not a peace treaty, leaving the US-led United Nations forces including South Korea, technically still at war with North Korea.

While South Korea had hoped an accord formally ending the conflict could have been unveiled on the sidelines of the UN General Assembly later this month, Moon’s security chief Chung Eui-yong said last week, without elaborating that the necessary conditions for a three-way meeting were missing.

Trump’s national security adviser John Bolton has also said he did not believe Kim would attend such a gathering.

Hopes of progress were revived however after Trump told reporters on Friday that a personal letter from Kim was on the way.

“It was a very warm, very positive letter,” Sanders said at Monday’s briefing.

“The primary purpose of the letter was to request and look to schedule another meeting with the president which we are open to and are already in the process of co-ordinating that,” she said.

Sanders told reporters the letter exhibited “a continued commitment to focus on denuclearisation of the peninsula.”

She said a military parade in Pyongyang on Sunday was “a sign of good faith” because it did not feature any long-range missiles.