U.S. President Donald Trump said Thursday that North Korea has already destroyed four of its big test sites on the road to "total denuclearization."

Trump was speaking at a Cabinet meeting following his historic meeting with North Korean leader Kim Jong-un in Singapore last week.

The two leaders agreed then that Kim would commit to "complete denuclearization" of the Korean Peninsula, while Trump committed to provide security guarantees to the regime.

"They've stopped the sending of missiles, including ballistic missiles. They're destroying their engine site. They're blowing it up," Trump said. "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 taking place."

It was unclear which test sites the president was referring to. In May North Korea demolished its only known nuclear test site in Punggye-ri, which included four testing tunnels.

It's possible Trump was referring to those four sites, although one of the tunnels was reportedly abandoned earlier.

This EPA file photo shows U.S. President Donald Trump. (Yonhap)

"They want to get it done. We want to get it done. And we're moving quickly," Trump added.

He also heaped praise on U.S. Secretary of State Mike Pompeo for doing a "fantastic" job on North Korea, joking that he was surprised to see him seated next to him.

"I thought he might have gone back to North Korea," said Trump.

Pompeo is expected to travel to Pyongyang within days for follow-up negotiations.

The deal also included North Korea's repatriation of the remains of American soldiers killed in the 1950-53 Korean War.

Speaking at a rally Wednesday night, Trump said the remains of 200 soldiers were sent back the same day, but he appeared to walk back those remarks.

"I understand ... that they've already sent back, or are in the process of sending back, the remains of our great heroes who died in North Korea during the war," he said. "And that's already in the process of coming back."

Trump thanked South Korean President Moon Jae-in, among other leaders, for being "terrific" with North Korea.

"He's been really moving it along and pushing as hard as they can," he said. "But without the United States, it had no chance whatsoever."

Moon has held two summits with Kim since April to push for denuclearization and the establishment of a permanent peace regime on the peninsula. (yonhap)

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