Kamala Harris embarked on a drive to exploit her strong debate performance on Thursday, as the Democratic presidential nominee’s campaign pledged to intensify efforts to persuade voters in battleground states deemed essential to winning the White House.

Meanwhile, her opponent Donald Trump – whose debate performance has been criticized even by some of his supporters – said that he would refuse to debate Harris again. “There will be no third debate,” he said in an angrily worded post on his Truth Social social media platform.

Basking in her debate win, the US vice-president travelled to the crucial swing state of North Carolina for rallies in Charlotte and Greensboro before heading north to Pennsylvania, another vital piece of the electoral battleground, where she is set to hold two more events on Friday.

Harris is locked in a knife-edge contests with Donald Trump across seven swing states that have become focal points in the campaign to win November’s poll. When Joe Biden was the Democratic nominee, Trump had established a firm lead in many of these states but Harris has now clawed back the gap and re-energized her party’s chances.

For his part, Trump – who has insisted he won Tuesday’s debate with Harris in Philadelphia, despite widespread doubts among his supporters – headed to Arizona, another state where the candidates are neck-and-neck, and which was narrowly won by Biden in the 2020 presidential election.

While most recent surveys have shown Harris with a narrow but consistent nationwide lead, November’s election result will almost certainly rest on which candidate prevails in the seven battleground states – with Michigan, Wisconsin, Georgia and Nevada also seen as vital.

“Seeking to capitalize on her decisive debate victory Tuesday night against Donald Trump, Vice President Kamala Harris is hitting the campaign trail to extend her momentum and further crystallize for voters the choice in the election that her debate performance made clear,” stated a memo from the Harris campaign released on Thursday.

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The memo said campaign staff had spent Wednesday poring over the 105-minute debate in a search for key moments that could be used for television and digital adverts that would be targeted at swing states.

It also pledged that Harris – who has been criticised for avoiding the media since becoming the Democrats’ nominee – would hold a series of interviews with local media in battleground states. That includes a scheduled meeting in Georgia next week with the National Association of Black Journalists, which hosted Trump in August in an encounter that turned into a public relations disaster for the Republican nominee.

Harris won broad praise for her display at Tuesday night’s debate, in which she was viewed as successfully baiting and laying traps for Trump – who, in turn, veered repeatedly off-message with broadsides about crowd sizes at his campaign rallies and a baseless rant about immigrants.

Some Trump supporters blamed his sub-par showing on the influence of Laura Loomer, a noted conspiracy theorist, who travelled with him to the debate and had promoted a false rumour about Haitian immigrants eating pet cats and dogs, which the ex-president then repeated in the midst of the encounter.

Authorities in Springfield, Ohio, where the practice was said to have been taking place, have dismissed the story – which appeared to have been spread on far-right internet forums and for which there is no evidence.

But in a sign of its continuing fallout, police were reported to have evacuated Springfield city hall on Thursday following a bomb threat.

Harris had demanded another debate with Trump and her campaign trolled him by posting the entire first event on X in the form of an “ad” – reflecting its confidence that she won the contest decisively. A snap CNN poll conducted immediately afterwards bore out that belief, with 63% of viewers seeing her as the victor.

But Trump’s social media post – in which he ranted often in all caps about a variety of issues and claimed to have won the debate – appeared to scrap any hope of a rematch. “KAMALA SHOULD FOCUS ON WHAT SHE SHOULD HAVE DONE DURING THE LAST ALMOST FOUR YEAR PERIOD. THERE WILL BE NO THIRD DEBATE!,” he said referring to the first debate as his face off with Biden and his contest with Harris as the second debate.

An estimated 67.1 million people watched the debate – nearly 16 million more than saw Trump’s contest with Biden in June.

Immediately after Tuesday’s event, Harris was endorsed by the pop megastar Taylor Swift, an announcement which prompted reportedly more than 337,000 people to visit a voter registration link that the singer posted on her Instagram account, according to the General Services Administration.

There was also fresh woe on Thursday for Trump when Alberto Gonzales, a former attorney general under George W Bush, became the latest Republican to endorse his opponent, invoking the Republican nominee’s incitement of the 6 January 2021 attack on the US Capitol when he was president.

“As the United States approaches a critical election, I can’t sit quietly as Donald Trump – perhaps the most serious threat to the rule of law in a generation – eyes a return to the White House,” Gonzales said in a statement. “For that reason, though I’m a Republican, I’ve decided to support Kamala Harris for president.”

He added: “Trump failed to do his duty and exercise his presidential power to protect members of Congress, law enforcement and the Capitol from the attacks [on January 6].”