The two camps had already agreed to one presidential debate on September 10 and a vice-presidential face-off on October 1, but the Trump campaign had been pushing for two further presidential debates in September and an extra VP encounter.

"The debate about debates is over. Donald Trump's campaign accepted our proposal for three debates -- two presidential and a vice-presidential debate," the Harris campaign said in a statement.

It added that "assuming Donald Trump shows up on September 10," Harris's running mate Tim Walz would debate Trump's VP pick J.D. Vance on October 1, and then there would be another Trump-Harris face-off later in October.

The Trump campaign did not immediately respond to an AFP request for its reaction to the statement.

Harris's late entry into the race -- replacing President Joe Biden after his withdrawal amid concerns over his age and unpopularity -- has effectively turned it into the kind of sprint to election day more common in Europe.

Already a trailblazer as the first female and first Black and South Asian vice president, Harris is aiming to make history as the first woman president -- and is scrambling to pitch herself to the public ahead of November 5.

She and Walz head to the Democrats' national convention in Chicago next week on the back of a blockbuster start, in which they have reversed Trump's polling leads, obliterated fundraising records and attracted huge ebullient crowds to their rallies.

CBS posted Wednesday on social media platform X that it had offered four potential vice-presidential debates in September and October to Walz, the governor of Minnesota, and Vance, a senator from Ohio.

Both accepted October 1, which comes after early voting has already started in several states, but Vance suggested an earlier debate on September 18 that he said had been offered by CNN.

He had earlier told Fox News he would not do "one of these fake debates... where they don't have an audience," like the June 27 encounter between Trump and Biden that effectively ended the Democrat's reelection campaign.

The Harris and Trump debate on September 10 will be hosted by ABC News, a channel the president had previously baulked at, saying he was in a legal dispute with its executives.