North Korea has already begun its denuclearization, US President Donald Trump said Thursday, after many observers greeted with skepticism the results of his historic meeting with the Norths leader Kim Jong Un and as officials said there was no such evidence since the summit last week. "Theyve already blown up one of their big test sites. In fact, it was actually four of their big test sites. And the big thing is, it will be a total denuclearization, which is already starting," Trump said at a cabinet meeting. Asked on Wednesday if North Korea had done anything toward denuclearization since the summit, US Defense Secretary Jim Mattis told reporters: “No, Im not aware of that ... obviously, its the very front end of a process. The detailed negotiations have not begun. I wouldnt expect that at this point.” Mattis sat next to Trump at Thursdays Cabinet meeting. The Pentagon did not immediately respond to a request for comment on Trumps latest remarks. There also was no immediate response from the White House. There had been contact with North Korean officials since the June 12 Trump-Kim summit, the US State Department said. US Secretary of State Mike Pompeo "will be meeting with them and talking with them at the earliest possible date" to implement what was agreed in Singapore, spokeswoman Heather Nauert told reporters, without providing further details. In late May, before the summit in Singapore, Pyongyang said it had fully demolished its only known nuclear test site. Foreign journalists invited to the Pungyye-ri test facility in North Hamgyong province described a series of explosions throughout the day, three of them in entry tunnels, followed by blasts that demolished a nearby barracks and other structures. Punggye-ri has been the staging ground for all six of the Norths nuclear tests, including the latest and by far most powerful one in September last year which Pyongyang said was an H-bomb. Experts are divided over whether the demolition will render the site inoperable. Skeptics say the facility has already outlived its usefulness with six successful nuclear tests and can be quickly rebuilt if needed. At their summit, Kim and Trump signed a pledge "to work towards complete denuclearization of the Korean Peninsula," a stock phrase favored by Pyongyang that stopped short of longstanding US demands for North Korea to give up its atomic arsenal in a "verifiable" and "irreversible" way.