He said on Thursday - two days after the pair's first showdown in Philadelphia - that Harris only wanted a rematch because he "clearly" won.

Several instant polls taken after Tuesday's contest indicated voters felt Harris had performed better than her Republican opponent.

Trump added that Harris should instead "focus" on her job as vice-president.

Shortly after, at a campaign rally in North Carolina, Harris responded by saying they "owe" voters another debate because "what is at stake could not be more important".

Polls suggest the two candidates are in an extremely tight race with just two months to go before the election.

Both claimed victory after Tuesday's 90-minute debate on ABC News, in which Harris rattled Trump with a string of personal attacks that put him on the defensive. These included comments about the size of his rally crowds and his conduct during the 6 January 2021 riot at the US Capitol.

Trump and his supporters have since accused the two ABC journalists that moderated the debate of being unfair and biased in favour of Harris. He said on Thursday that he did not need another debate.

"When a prizefighter loses a fight, the first words out of his mouth are 'I want a rematch'," Trump wrote in a lengthy Truth Social post on Thursday.

"Polls clearly show that I won the debate against comrade Kamala Harris, the Democrats' radical left candidate... and she immediately called for a second debate," he added.

The former president held a rally in Arizona on Thursday and gave an interview with Telemundo Arizona backstage. "We just don't think it's necessary," he said of a second debate with Harris. "We think we've discussed everything and I don't think they want it either."

The Harris campaign, however, called for a second debate immediately after Philadelphia and continued to do so on Thursday. They said voters "got to see the choice they will face at the ballot box: moving forward with Kamala Harris or going backwards with Trump".

"Vice-President Harris is ready for a second debate. Is Donald Trump?" the campaign said.

Speaking after the debate, various Trump campaign surrogates - including Florida Republican Representative Matt Gaetz - said they believed Trump would welcome another debate.

However, Trump said on Fox News the following morning that the debate had been "rigged" and that he was "less inclined" to attend another after his "great night".

His decision on Thursday also appeared to contradict earlier messaging from his own campaign. On Wednesday morning, Jason Miller, a senior adviser to the former president, told CNN that Trump “has already said that he is going to do three debates".

Both campaigns had reportedly been in discussions over a debate on NBC News on 25 September. The network has not commented on Trump's latest statement.

Adam Green, the co-founder of the Progressive Change Campaign Committee - an organisation that has advised the Harris-Walz campaign on economic messaging - told the BBC that Trump's decision was a "double favour" to the Harris campaign.

"Voters will have a lasting impression of Kamala Harris as looking presidential and standing on their side," he said. "That will probably do her very well."

"Another debate would potentially help Harris, but could also shake up the existing glow that surrounds her," Mr Green added.

Jeremy Petersen, an independent voter from Utah, told the BBC that he was not surprised by Trump's decision.

"If [Trump] doesn't feel like he can score some social media soundbites, there's no benefit for him to show up," said Mr Petersen, who added that he would probably support Harris after the Philadelphia debate.

"He felt that Harris wouldn't have the type of performance she did and now he's running scared," Mr Petersen added. "He can't stop her momentum via debate so he needs a new angle."

Televised debates date back to 1960, when John F Kennedy faced off against Richard Nixon.

There are traditionally two or three presidential debates happening in most election cycles, along with at least one vice-presidential debate.

That tradition, however, was upended in July, when Joe Biden withdrew from the election weeks after a disastrous performance against Trump in the first debate.

The subsequent debate between Harris and Trump followed weeks of back and forth over whether it would go ahead, and under what conditions.

Trump previously suggested additional debates on Fox and NBC News, although Harris only agreed to ABC.

In his Truth Social post on Thursday, Trump said his rival "refused" to do the additional debates.

Statistics from media analytics firm Nielsen show that 67.1m people watched the debate, a significantly higher figure than the 51.3m who tuned into the June debate between Trump and Biden.

Polls suggest Harris and Trump are in an extremely tight race in the key battleground state of Pennsylvania, Michigan and Wisconsin.

A Reuters/Ipsos poll on Thursday indicated Harris had a five-point lead over Trump nationally, while 53% of respondents said that she won Tuesday's debate.