WASHINGTON — President Joe Biden and former President Donald Trump on Wednesday agreed to hold two campaign debates — the first on June 27 hosted by CNN and the second on Sept. 10 hosted by ABC — setting the stage for their first presidential face-off to play out in just over a month.

The quick agreement on the timetable followed the Democrat’s announcement that he would not participate in fall presidential debates sponsored by the nonpartisan commission that has organized them for more than three decades. Biden’s campaign instead proposed that media outlets directly organize the debates between the presumptive Democratic and Republican nominees.

The debate is so unusually early on the political calendar that neither Biden nor Trump will have formally accepted his party’s nomination.

Hours later, Biden said he had accepted an invitation from CNN, adding, “Over to you, Donald.” Trump, who had insisted he would debate Biden anytime and anyplace, said on Truth Social he’d be there, too, adding, “Let’s get ready to Rumble!!!” Soon after that, they agreed to the second debate on ABC.

“Trump says he’ll arrange his own transportation,” Biden wrote on X, working in a jab about the perks of incumbency. “I’ll bring my plane, too. I plan on keeping it for another four years.”

The swiftness with which the match-ups came together reflects how each of the two unpopular candidates thinks he can get the better of his opponent in a head-to-head showdown. Trump and his team are convinced the debates will exacerbate voters’ concerns about Biden’s age and competence, while Biden’s team believes Trump’s often-incendiary rhetoric will remind voters of why they voted him out of the White House four years ago.

The presidential debates, always a critical moment on the political calendar, could be particularly important in a year when voters are underwhelmed with their choices and have expressed concerns about the candidates’ advanced ages — Biden is 81 and Trump 77.

Sprightly on social media, the rivals traded barbs — each claiming victory the last time they faced off in 2020.

“Donald Trump lost two debates to me in 2020, since then he hasn’t shown up for a debate,” Biden said in a post on X. “Now he’s acting like he wants to debate me again. Well, make my day, pal.”

Trump, for his part, said Biden was the “WORST debater I have ever faced – He can’t put two sentences together!”

The June debate is likely to cap a busy and unsettled stretch, following the likely conclusion of Trump’s criminal hush money trial in New York, foreign trips by Biden to France and Italy, the end of the Supreme Court’s term, and the expected start of two criminal trials for the president’s son, Hunter Biden.