Washington remained committed to the "complete, verifiable and irreversible" denuclearisation of North Korea, Pompeo added, after the historic US-North Korea summit in Singapore drew criticism for its vague wording on plans for Pyongyang to give up its nuclear weapons.

"We believe that Kim Jong Un understands the urgency... that we must do this quickly," he said of the effort to have North Korea abandon its atomic arsenal.

Washington's top diplomat was in Seoul to brief his South Korean and Japanese counterparts after President Donald Trump's post-summit comments sparked confusion and concern in Tokyo and Seoul.

But Pompeo insisted at a joint press conference with the two countries' foreign ministers that there was no daylight among the allies on how to achieve the denuclearisation of North Korea.

Contrasting the Trump policy with previous US administrations, Pompeo said: "In the past, they were providing economic and financial relief before... complete denuclearisation had taken place."

"That is not going to happen, President Trump made that clear."

Pompeo's comments came after North Korean state media reported Wednesday that Trump had not only offered to stop military exercises during dialogue, but also lift sanctions imposed on Pyongyang.

Trump said after his meeting with Kim -- the first between sitting US and North Korean leaders -- that Washington would halt its joint military exercises with South Korea, an announcement that caught Seoul -- and apparently the Pentagon -- by surprise.

The US and South Korea conduct several large drills every year to maintain readiness for operations on the peninsula, a source of irritation for Pyongyang, which considers them preparations for an invasion.

- 'Frank' discussions -

South Korean Foreign Minister Kang Kyung-wha appeared to sidestep the issue at the joint press conference, saying the matter would be left to military authorities to discuss, and that the US-South Korea alliance remained "as robust as ever".

Earlier, South Korean President Moon Jae-in acknowledged that "there may be very conflicting views" about the summit, but it had still helped mitigate fears of a nuclear war.

"In this way I believe it was very successful."

He later said Seoul would carefully consider the future of the drills "if North Korea faithfully implements denuclearisation measures and sincere dialogue continues", according to his office.

While it is not directly involved, Japan also considers the exercises vital.

The "deterrence based on them (plays) an essential role for security in northeast Asia", Japanese Foreign Minister Taro Kono said after the "frank" trilateral talks Thursday.

Kono said Japan understood the pause in the drills to be contingent on North Korean steps towards denuclearisation, adding that "no security guarantees have been given yet".

Pompeo said the suspension of the exercises depended on productive negotiations in "good faith".

Trump had raised eyebrows Tuesday by describing his own country's drills on the Korean peninsula as "provocative", a term used by the North for the exercises.

Pyongyang describes its nuclear weapons and long-range missiles as a shield against US aggression, and has in the past linked denuclearisation to the removal of US forces from the peninsula.

Pompeo later left Seoul for China, arriving late afternoon local time in Beijing where he is scheduled to meet President Xi Jinping and Foreign Minister Wang Yi.

- 'Sleep well tonight!' -

Despite some concerns among allies and analysts, the Trump administration continues to tout the summit as a success, and Pompeo said earlier that he hopes to see "major disarmament" of North Korea by 2020.

A bullish Trump declared the nuclear threat from North Korea no longer exists, and tweeted Wednesday that people "can now feel much safer than the day I took office" and can "sleep well tonight!"

The US leader also defended his decision on the military drills with South Korea: "We save a fortune by not doing war games, as long as we are negotiating in good faith -- which both sides are!"

The president's latest comments are in stark contrast to his threats to unleash "fire and fury" last year in response to Pyongyang's nuclear and long-range missile tests. The North retaliated by boasting it could annihilate the United States.

After months of tensions which saw Trump and Kim trade personal insults, whirlwind diplomatic efforts were launched earlier this year, catalysed by the Winter Olympics in South Korea.

The remarkable de-escalation saw Kim reach out to Trump, conduct a historic summit with South Korean President Moon Jae-in, and visit Xi in Beijing -- his first trip abroad as leader.

In the latest step to ease cross-border tensions, the two Koreas held their highest-level military talks in over a decade on Thursday at the truce village of Panmunjom in the Demilitarized Zone that divides the two countries.

The reclusive regime in Pyongyang has long craved international legitimacy, and has played up the summit as a major victory for Kim, with state media calling it the "meeting of the century".