Kamala Harris laid down another challenge to Republican rival Donald Trump to meet her for a second debate before November’s presidential election, telling supporters in New York that her opponent “seems to be looking for an excuse” to avoid a second confrontation.

On Saturday, the vice-president and Democratic nominee said she had accepted an invitation from CNN to debate the former president, but Trump said it was already “too late”.

In her remarks at a New York fundraiser, Harris doubled down in her taunting of Trump over the issue, saying: “I think we should have another debate.”

“I accepted an invitation to debate in October, which my opponent seems to be looking for an excuse to avoid when he should accept,” she added. “He should accept because I feel very strongly that we owe it to the American people, to the voters, to meet once more before election day.”

The question of the US’s high stakes presidential debates has hung over the candidates since Joe Biden dropped out of the race following a disastrous performance in June. The single scheduled debate between Trump and Harris, earlier this month, was widely viewed to have gone Harris’s way and been a serious blow to Trump.

But it did not move the polls as much as the Harris campaign hoped and her campaign is still tasked with introducing her to US voters. Last week, Harris went on Oprah to help smooth the introduction along.

This week Harris is due to reveal a set of new economic policies. Polls show she is steadily gaining trust on the key issue of the economy, which often favors Trump and the Republican party.

On Sunday, Harris returned to the key themes of the message Democrats wish to underline – a threat to democracy they perceive a second Trump terms represents and the knife-edge that polls suggest the race remains balanced upon.

“This is a man who said he would be a dictator on day one … just imagine Donald Trump with no guardrails,” Harris said in New York. “This race is as close as it could be. This is a margin of error race … and I am running and we are running as the underdog.”

Harris called Trump an “unserious man”, but said the consequences of putting him back in the White House were “very serious”.

Head-to-head polls tend to show Harris with a narrow but solid lead over Trump, though the situation is more mixed in the crucial swing states that will decide the race to the White House. That is a reverse of the situation when Biden was in the race, where Trump had established a firm lead over the US president.