China on Thursday derided the "irresponsible and absurd logic" of the United States after President Donald Trump accused Beijing of making Washington's relationship with North Korea more difficult.

Trump doubled down on his suggestion that China was not helping to rein in its Cold War-era ally -- a charge he first levelled when he cancelled a trip to North Korea by Secretary of State Mike Pompeo that was due to take place this week.

"A lot of people, like me, feel that the US is first in the world when it comes to twisting the truth, and irresponsible and absurd logic," Chinese foreign ministry spokeswoman Hua Chunying told a regular press briefing.

"This logic is not easily understood by all," Hua said.

Trump's refusal to direct criticism at North Korean leader Kim Jong Un and instead blame other parties for a lack of progress comes despite reports the US received a belligerent letter from Pyongyang, which prompted Secretary of State Mike Pompeo to cancel a planned trip to North Korea last weekend.

"We hope the US can play a positive and constructive role in settling the issue just like the Chinese. To solve the problem, it should look at itself instead of shifting blame," Hua added.

- Trade war -

Speaking at the White House on Wednesday, Trump said: "China makes it much more difficult in terms of our relationship with North Korea".

"Part of the North Korea problem is caused by the trade disputes with China," Trump said.

But he insisted his ties with Chinese President Xi Jinping were "great" and that he had a "fantastic relationship" with North Korean leader Kim Jong Un, whom he met in Singapore in June.

The US president said he was not considering resuming joint military exercises on the Korean Peninsula that Pyongyang considers "provocative."

Beijing is Pyongyang's sole major ally, and the main transit country for any goods entering the North. Trump said that China -- angered by US moves on trade -- is no longer being as tough as it could be on North Korea.

"We know that China is providing North Korea with considerable aid, including money, fuel, fertilizer and various other commodities. This is not helpful!" he tweeted on Wednesday evening.

On the subject of military exercises, which the US suspended as a "good faith" measure following Trump's summit with Kim, the president said "there is no reason at this time to be spending large amounts of money on joint US-South Korea war games" though added these could resume if the need arose.

It came a day after Defense Secretary Jim Mattis said the Pentagon was not planning to suspend any more military drills, before appearing to backtrack on Wednesday by insisting "no decisions" had been made on the matter.

Trump also reiterated his wish to fundamentally alter the trade status quo between the United States and China, the world's top two economies.

He said he needed to take a tough stance with Beijing on trade "because it was really not fair to our country," criticising his predecessors who "closed their eyes" to the issue.

- Belligerent letter -

In June, Trump and Kim pledged to work toward the "complete denuclearisation of the Korean Peninsula" although their joint statement was short on details for how that might be achieved.

Efforts stalled several weeks ago, and last week, Trump ordered Secretary of State Mike Pompeo to cancel a planned trip to Pyongyang. At the time, Trump said that he did not believe China was helping in the denuclearisation process due to Washington's tougher stance on trade.

Pompeo said Tuesday that Washington remains ready to engage "when it is clear that Chairman Kim stands ready to deliver on the commitments that he made at the Singapore summit to President Trump to completely denuclearise North Korea".

According to the Washington Post, Pyongyang sent Pompeo a belligerent letter that prompted him to cancel the visit, though its precise contents were not known.

US news site Vox meanwhile reported that Trump at June's summit pledged to sign a declaration ending the Korean War, and now the two countries remain deadlocked over who will follow through on their commitment first.

On Wednesday, State Department spokeswoman Heather Nauert told reporters that Washington believes "denuclearisation has to take place before we get to other parts," confirming that included such a declaration.