"They've 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.

In late May, before the June 12 Trump-Kim 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 North's 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.

The summit pledge was followed by the US military's postponement of major joint exercises with its ally South Korea following a pledge by Trump to halt the drills which have aroused repeated anger in the North.

Trump and Kim also agreed on the repatriation of the remains of American soldiers killed during the 1950-1953 Korean War.

The president said at the cabinet meeting that "they've already sent back, or are in the process of sending back, the remains."

A US official had said Tuesday that Pyongyang may soon begin returning remains from among up to 200 sets the North says it has recovered.