The US secretary of state Mike Pompeo at a press conference earlier this year (Picture: US Dept of Defense).
North Korea is far from living up to its pledge to denuclearise and remains in violation of numerous UN Security Council resolutions, according to the US secretary of state.
Speaking before he attended an Asian security forum with North Korea's foreign minister, Mike Pompeo told reporters in Singapore there was "still a ways to go" in order to achieve the goal of ridding the North of its nuclear weapons.
His comments came after the White House announced President Donald Trump had received a new letter from North Korean leader Kim Jong Un and responded quickly with a letter of his own.
Mr Pompeo has taken the lead in negotiations with the North, having travelled to Pyongyang three times since April and accompanied Mr Trump to the summit, and he will be in the same room on Saturday as his North Korean counterpart at the Association of South East Asian Nations annual regional forum.
A separate meeting between the two is possible but not confirmed, according to State Department officials.
"Chairman Kim made a commitment to denuclearise," Mr Pompeo told reporters accompanying him to Singapore from Kuala Lumpur, Malaysia.
"The world demanded that (he) do so in the UN Security Council resolutions. To the extent they are behaving in a manner inconsistent with that, they are in violation of one or both the UN Security Council resolutions, we can see we still have a ways to go to achieve the ultimate outcome we're looking for."
On Thursday, Mr Trump tweeted his thanks to the North Korean leader "for your nice letter - I look forward to seeing you soon!"
The White House did not provide details on the content of the letter from Mr Kim, received on Wednesday, or of Mr Trump's reply.
Spokeswoman Sarah Huckabee Sanders said the letters addressed their commitment to work toward North Korea's "complete denuclearisation".
Ms Sanders said no second meeting is "locked in" as a follow-up to the Singapore summit in June, but they remain open to discussions.
Vice president Mike Pence and US military leaders received the remains in Hawaii during a sombre ceremony on Wednesday.
Last week, a US research group said North Korea had started dismantling key facilities at its main satellite launch site.
However, North Korea is suspected to be building new missiles, it emerged this week, casting doubt on Trump's claims of victory last month.