Defense Secretary James Mattis on Wednesday said he is "not aware" of any steps North Korea has taken yet to denuclearize following the historic summit between President Trump and North Korean leader Kim Jong Un.

"I'm not aware of it," Mattis told reporters outside the Pentagon when asked if there are any military indications North Korea has done anything to denuclearize.

"Obviously, at the very front end of the process," he continued. "The detailed negotiations have not begun. I wouldn't expect that at this point."

Trump and Kim met in Singapore last week. The two leaders signed a joint statement that committed North Korea "to work toward complete denuclearization of the Korean Peninsula."

The statement included no specifics on how that will be achieved, including no timeline for nuclear dismantlement and steps for verification.

Following the summit, Trump declared that North Korea was "no longer a nuclear threat" despite the exact terms of the agreement remaining unclear.

The document named Secretary of State Mike Pompeo as the lead U.S. negotiator going forward. On Monday, Pompeo, who twice traveled to Pyongyang in the lead up to the summit, said he'd "likely travel back before too terribly long."

On Wednesday, Mattis said he will travel to Beijing and Seoul next week.

"Usual close coordination, ongoing as we sort out the way ahead," Mattis said. "Everything is going fine between us and Republic of Korea, specifically between the chairman [of the Joint Chiefs of Staff] and his counterpart, between myself and my counterpart."

He also said a meeting with national security adviser John Bolton to discuss joint U.S.-South Korea military exercises will happen Friday at the Pentagon. The Defense Department announced Monday it was suspending planning for the August exercise in line with Trump's announcement after the summit.

Asked about the suspension's effect on military readiness, Mattis said, "we'll sort it all out."

"I need to sort it out before I start talking about it," he said.

The Trump-Kim statement also committed to recovering the remains of U.S. service members killed in the Korean War. The Pentagon estimates there are about 7,700 unaccounted-for Americans who fought in the war, which is still technically ongoing because it ended with an armistice in 1953. Of that, about 5,300 are believed to be in North Korea.

Mattis said discussions about returning the remains are "ongoing."

"I don't have any update for you," he said. "I know that we're engaged on it."