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North Korea's leader Kim Jong Un walks with U.S. President Donald Trump during a break in talks at the historic US-North Korea summit at the Capella Hotel on Sentosa Island, Singapore, June 12, 2018. SAUL LOEB/AFP/Getty Images

Citing a message sent to U.S. President Donald Trump, a senior diplomatic source told South Korea’s Yonhap news agency Tuesday that North Korean leader Kim Jong Un was willing to allow nuclear site inspection.

“I understand that Chairman Kim told (South Korean) President Moon (Jae-in) during their summit in September that if the U.S. took corresponding steps he would not only be willing to shut down the Yongbyon nuclear facilities but also allow verification,” the source said.

Moon relayed the message to Trump when the two leaders met during the United Nations General Assembly in New York in September, the source added.

Though Kim had previously expressed his willingness to shut down the nuclear site, there were no reports of him agreeing to allow inspectors in to verify the site.

"Chairman Kim's willingness to allow verification signals his intention to lay down all of his nuclear weapons and facilities, which could brighten the prospects for nuclear negotiations," said Shin Beom-chul, a national security analyst at the Asan Institute for Policy Studies in Seoul.

He recalled the last time North allowed foreign inspectors was in 2009. However, it had allowed only interviews and document reviews and refused on-site sampling. This decision had led to the collapse of the six-party nuclear talks.

"If Chairman Kim means the same level of verification as in 2008, there will still be obstacles ahead. But if it includes sampling and random inspections, that would be a very positive step,” said Shin.

When asked whether there have been new developments, U.S. State Department spokeswoman Heather Nauert said she was “not aware of any of that.” She, however, said Kim had agreed to inspections in a recently held meeting with Secretary of State Mike Pompeo, Reuters reported.

"That's something the secretary and Chairman Kim had agreed to and spoken about when the secretary was in Pyongyang about a month ago or so. So that's something they agreed to and we look forward to Chairman Kim fulfilling his commitments,” she said.

In October, reports suggested that North was preparing several of its nuclear and missile test sites for international inspections.

“Signs have been detected that North Korea is doing some preparations and intelligence-related activity over a possible visit by outside experts, as it shut down the nuclear test site and demolished some of the missile launching facilities at Dongchang-ri," Kim Min-ki of South Korea's ruling Democratic Party said at the time.

A month before that, President Moon also said Kim had agreed to allow international inspectors to observe a "permanent dismantlement" of key missile facilities. This step was in response to the U.S. demands that North had to take steps to fully close its nuclear and missile facilities before it agrees for easing of international sanctions.