Republican nominee Donald Trump said on Thursday he would not participate in another presidential debate against Kamala Harris ahead of the U.S. Nov. 5 election, after several polls showed his Democratic rival won their debate earlier this week.

"THERE WILL BE NO THIRD DEBATE!" the former president wrote on his social media site Truth Social.

Although Trump touted his performance on Tuesday against Harris, six Republican donors and three Trump advisers who spoke to Reuters earlier this week said they thought Harris had won the debate largely because Trump was unable to stay on message.

The debate attracted more than 67 million television viewers, according to early Nielsen data.

Harris, speaking at a rally shortly after Trump's post went live, said: "I believe we owe it to the voters to have another debate." In an earlier show of confidence, her campaign challenged Trump to a second debate almost immediately after Tuesday's showdown was over.

While Trump said in his post that polls showed he won the debate, several surveys showed that respondents thought Harris did better.

Among voters who said they had heard at least something about Tuesday's debate, 53 per cent said Harris won and 24 per cent said Trump won, according to a Reuters/Ipsos poll released on Thursday.

WATCH | Harris campaign wants another debate:

Trump, Harris both claim victory in debate

The campaigns for Donald Trump and Kamala Harris both claimed victory after Tuesday night's U.S. presidential debate, but many analysts point to the Democratic nominee as the winner of the night for her dominant performance, repeatedly needling Trump and knocking him off script.

The poll showed that 54 per cent of registered voters believed that the single debate between Trump and Harris was enough, while 46 per cent had wanted a second debate.

A majority of debate watchers said Harris outperformed Trump, according to a CNN flash poll released shortly after the debate. YouGov showed 54 per cent of those surveyed said Harris won while 31 per cent said Trump was the victor.

Trump had participated in a debate against President Joe Biden in June before his debate against Harris on Tuesday. Biden's halting performance overshadowed Trump's litany of falsehoods during that meeting, which led to internal party pressure and Biden's dropping from the race on July 21.