US President Joe Biden challenged Donald Trump Wednesday to "make my day" and hold two televised debates in June and September, with his Republican rival swiftly accepting.

Biden however shunned the three debates proposed by the bipartisan US election debates commission, opting instead for two audience-free clashes hosted by news organizations.

"Donald Trump lost two debates to me in 2020. Since then, he hasn't shown up for a debate. Now he's acting like he wants to debate me again. Well, make my day, pal," Biden said in a video on X, formerly Twitter.

"I'll even do it twice."

Biden also trolled Trump over his ongoing criminal hush money trial in New York, which features a mid-week break, adding: "So let's pick the dates Donald. I hear you're free on Wednesdays."

The Democrat and the Republican have been sparring for months over debates, for years a traditional part of any US presidential election campaign, but there has been uncertainty over whether they would go ahead. 

Trump —  who avoided any debates with his rivals for the Republican presidential nomination this year —  said he was "ready to Rumble!!!"

"I am Ready and Willing to debate Crooked Joe at the two proposed times in June and September," Trump said on his TruthSocial platform.

Describing Biden as "the WORST debater I have ever faced," Trump called for a "very large venue, although Biden is supposedly afraid of crowds."

Biden's campaign simultaneously sent a letter to the US election debates commission saying it rejected its calendar for three debates in September and October.

Instead Biden "plans to participate in debates hosted by news organizations," said the letter from campaign chief Jen O'Malley Dillon.

She added that the current, years-old structure was "out of step with changes in the structure of our elections and the interests of voters."

Biden's campaign proposed the first one-on-one debate in late June "after Donald Trump's New York criminal trial is likely to be over and after President Biden returns from meeting with world leaders at the G7 Summit."

The second should be in early September, which the Biden campaign said would be in time to influence early voting but would not keep candidates off the campaign trail in the "critical late September and October period."

The letter also proposed strict rules for the debates including keeping candidates' microphones off when it was outside their allotted time, to avoid candidates talking over each other.