By Angela Dewan and James Griffiths, CNN

(CNN) -- US Secretary of State Mike Pompeo said Monday that North Korean leader Kim Jong Un is ready to allow international inspectors into a key nuclear testing site, signaling a step forward in Pyongyang's commitment to denuclearizing the Korean Peninsula.

After meeting with Kim in Pyongyang on Sunday, Pompeo told journalists in Seoul that the leader had agreed to open up the Punggye-ri nuclear testing site to inspectors, according to a pool report. North Korea claims to have destroyed the site.

When asked for a date on the inspection, Pompeo responded: "As soon as we get it logistically worked out. Chairman Kim said he's ready to allow them to come in. There's a lot of logistics that will be required to execute that."

Pompeo said he was hopeful that Kim would allow inspectors to visit a "missile engine test site," believed to be a facility in the town of Tongchang-ri that North Korea says it has begun dismantling.

Pyongyang in May failed to follow through with its promises to allow inspectors to assess its demolition of Punggye-ri in what has become a roadblock in the country's denuclearization commitment, which was reiterated in June after a meeting between Kim and US President Donald Trump in Singapore.

Since Trump and Kim met, US-North Korea relations have stalled. Trump canceled Pompeo's planned trip to Pyongyang in August, citing little evidence that North Korea had followed through on any of its commitments to denuclearize.

Pompeo told reporters that a second summit between Trump and Kim was "pretty close."

"We are not quite there yet. But we will get there," Pompeo said. "We will be having more frequent and higher level working level group discussions than we have had in some time."

Pompeo appeared alongside South Korean President Moon Jae-in, who said a second US-North Korea summit would provide a chance to take "a decisive step forward in the denuclearization and peace process on the Korean Peninsula."