Joe Biden and Donald Trump agreed on Wednesday to hold a first presidential debate in June after the Democratic incumbent challenged his rival to "make my day" and the scandal-plagued Republican quickly responded he was ready to "rumble."

CNN announced it will hold the first debate on June 27 in Atlanta, Georgia. Biden proposed a second debate for September and Trump accepted.

Biden, 81, had set out his own terms for the debates with political showman Trump, such as time limits for speakers and having no live audience – a condition CNN said it had agreed to.

In his first formal debate offer after months of stalling, the Democrat also shunned the traditional calendar proposed by the commission that has run debates since 1988 as he sought to exercise control over the format.

Trump, 77, accepted the dates even as he set out a starkly different vision with a larger venue for "excitement purposes" and accused the Democrat of being afraid of crowds.

"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.

"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."

CNN said in a statement that the debate would be held at its studios in Atlanta in the "crucial battleground state of Georgia."

"To ensure candidates may maximise the time allotted in the debate, no audience will be present. Moderators for the debate and additional details will be announced at a later date," it said.

Biden's debate offer appeared to show him taking the calculated risk of putting Trump back into American living rooms ahead of November's election, hoping it could reverse the Republican's poll lead in a series of battleground states.

The Biden campaign has increasingly been trying to remind voters of what they say is the true face of the mercurial president who lost in 2020, amid what they fear is Trump "nostalgia" in some quarters – even as the Republican details his stark vision for an authoritarian second term in various interviews.

For his part, Trump has previously said he would debate his rival "anytime, anywhere" as he seeks to portray Biden as old and incapable of leadership.

After Biden's challenge, Trump – who avoided any debates with his rivals for the Republican presidential nomination this year – said he was "ready to Rumble!!!" for the proposed June and September debates. (AFP)