US President Donald Trump is insisting he has evidence that China is attempting to meddle in the US mid-term elections — but that it "respected" his "very, very large brain".

Despite damage control efforts by his administration, Trump repeated his claims that China is trying to meddle in the upcoming midterm elections because they oppose his tough trade policies.

"They do not want me or us to win, because I am the first president to challenge China on trade," Trump said. "And we are winning on trade. We are winning at every level.

"They would like to see me lose an election because they've never been challenged like this."

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Trump addressed a roomful of hundreds of reporters from US and international media organisations this morning in a sweltering hotel ballroom following his participation in UN talks.

He was particularly vocal on China and President Xi Jinping.

"He's a friend of mine," President Trump said of China's president-for-life.

"He may not be a friend of mine anymore".

Nevertheless, Trump insisted he maintained a strong influence over the rapidly emerging world power.

The president added that China "has total respect for Donald Trump and for Donald Trump's very, very large brain".

Laughing matters

President Trump rejected the notion that the UN General Assembly had laughed at his opening statement that his government had been an incomparable 'success'.

"People had a good time with me. We were doing it together, we had a good time."

"We had fun," Trump said. "That was not laughing at me. So the fake news said 'people laughed at President Trump.' They didn't laugh at me, people had a good time with me. We were doing it together, we had a good time."

Trump opened Tuesday's speech by boasting about an American economy that he says is "booming like never before." He also claimed his administration had accomplished more in the less than two years he's held office than any other administration at the same point.

His boast elicited laughter from the audience.

Damage control undone

At the news conference in New York, a reporter asked Trump what evidence he has to back up the accusation of election interference, which China has denied.

President Trump simply asserted that "we have evidence" but "I can't tell you now."

He says his allegation did not come "out of nowhere."

The Trump administration says China is stepping up covert and overt activities to stifle free speech, punish those who support the president's tough trade stance against China and interfere in the US political system. The administration says China is hurting farmers and workers in pro-Trump states and districts.

According to Trump, China has "actually admitted that they're going after farmers."

"I don't like it when they attack our farmers and I don't like it when they put out false messages. But beside that, we learned that they are trying to meddle in our elections and we're not going to let that happen just as we're not going to let that happen with Russia."

Earlier, at the Pentagon, Defense Secretary Jim Mattis said he thinks the current tensions with China will be overcome because both countries value the relationship.

He said he is not sure what to make of China's rejection of a Hong Kong port visit by a US Navy ship. China also cancelled plans for its navy chief to meet with his American counterpart at the Pentagon this week. Mattis said this and other problems with China are being "sorted out." Mattis told reporters he does not believe the current tensions amount to a fundamental shift in the relationship.

His comments came after President Donald Trump earlier accused the Chinese of "attempting to interfere" in the November elections. China denied this.

Frosty Canada relations

President Donald Trump says he has rejected a one-on-one meeting with Canadian Prime Minister Justin Trudeau over the tariff dispute involving the two countries.

He's also threatening to place tariffs on cars imported from Canada as trade talks between the two neighbours drag on.

Trump says during a news conference in New York that Canada has treated the US "very badly" during the trade talks.

Canada was left out when the United States and Mexico reached an agreement last month to revamp the North American Free Trade Agreement.

The US and Canada are under pressure to reach a deal by September 30. Trump is suggesting he may go forward with a revamped NAFTA without Canada. The president says it would be called "USM," for the US and Mexico, instead of "USMC."