SEOUL/WASHINGTON (Reuters) - U.S. 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 is looking at scheduling one, White House spokeswoman Sarah Sanders said on Monday.

The two countries have been discussing North Korea’s nuclear programs since their leaders met in Singapore in June, although that summit’s outcome was criticized for being short on concrete details about how and whether Kim is 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 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 U.S.-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 U.N. 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 coordinating that,” she said.

Sanders told reporters the letter exhibited “a continued commitment to focus on denuclearization 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.

In South Korea, officials nurtured hope that next week’s inter-Korean summit could provide renewed momentum to nuclear negotiations, after last month’s setback when Trump canceled a visit to Pyongyang by Secretary of State Mike Pompeo due to a lack of progress.

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South Korea’s President Moon is expected to present some proposal to Kim suggesting phased steps toward denuclearization and U.S. security guarantees including an official end to the Korean War. Moon could then discuss the idea when he meets Trump during the U.N. General Assembly meeting in New York later this month, South Korean officials said.

Trump asked Moon to act as “chief negotiator” between Washington and Pyongyang during their phone call last week, Moon’s spokesman Kim Eui-kyeom told reporters.

“In order for us to move toward the next level of dismantling North Korea’s existing nuclear weapons, the leaders of North Korea and the United States once again must have big ideas and take bold decisions,” Moon told a cabinet meeting on Tuesday.

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“North Korea should abolish its nuclear programs, and the

United States foster such conditions with corresponding action.”

WINDOW OF OPPORTUNITY

The nuclear envoys of South Korea and the United States also held a meeting on Tuesday as part of efforts to jumpstart stalled nuclear talks between Pyongyang and Washington.

Lee Do-hoon, South Korea’s nuclear negotiator, told reporters that he and his U.S. counterpart Stephen Biegun discussed how to bring progress on the North’s denuclearization and establishing peace on the Korean peninsula.

“We take this very seriously, the responsibility that is on both of us,” Biegun told Lee at the start of the talks.

“But we also have a tremendous opportunity created by President Trump, by President Moon and by Chairman Kim. We need to do everything we can to make the most of this moment of opportunity.”

Harry Kazianis, director of defense studies from the Centre for the National Interest, a think tank in Washington reckoned Trump was right to pursue a second meeting with the North Korean leader .

“When you combine Kim’s pledge to denuclearize by the end of Trump’s first term, as well as not displaying any long-range ballistic missiles during the north’s recent 70th anniversary celebrations, there are reasons for optimism,” he said.

(This version of the story was refiled to fix subhead)