Secretary of State Mike Pompeo Michael (Mike) Richard PompeoTreasury sanctions individuals, groups tied to Russian malign influence activities Navalny released from hospital after suspected poisoning Overnight Defense: Pentagon redirects pandemic funding to defense contractors | US planning for full Afghanistan withdrawal by May | Anti-Trump GOP group puts ads in military papers MORE said after a meeting with North Korean leader Kim Jong Un on Sunday that Washington and Pyongyang "continue to make progress" toward denuclearization, but did not provide details.

"[W]e had a good, productive conversation,” Pompeo told South Korean President Moon Jae-in when asked how the secretary of State's meeting went, according to The Associated Press.

“As President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE said, there are many steps along the way and we took one of them today. It was another step forward. So this is, I think, a good outcome for all of us.”

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Pompeo also told Moon that Kim agreed to meet with Trump at a summit that "should be held as soon as possible," according to a statement the South Korean leader's office issued later.

Moon's office also indicated that the U.S. and North Korea are still discussing when and where the meeting will be held.

Trump, meanwhile, said in a tweet that he looks forward to seeing Kim in the "near future."

.@SecPompeo had a good meeting with Chairman Kim today in Pyongyang. Progress made on Singapore Summit Agreements! I look forward to seeing Chairman Kim again, in the near future. pic.twitter.com/bUa2pkq80s — Donald J. Trump (@realDonaldTrump) October 7, 2018

Pompeo met with Kim for three and a half hours on Sunday, according to a pool report from the only U.S. journalist accompanying Pompeo in Asia, the AP reports.

The secretary of State has repeatedly refused to discuss the details of negotiations between the two countries.

Trump has touted the progress both countries have made, but has reportedly become frustrated at the lack of forward momentum toward denuclearization.

North Korean Foreign Minister Ri Yong Ho has said the country cannot proceed toward giving up its nuclear capabilities without "trust in the U.S." and that without that, "there is no way we will unilaterally disarm ourselves first."

— This report was updated at 10:45 a.m.