In a letter Thursday to Bush campaign chairman Marc Racicot, Kerry campaign chairwoman Jeanne Shaheen said holding debates now would allow voters "the honest dialogue they deserve."
In response, Bush campaign spokesman Scott Stanzel said Kerry first has to end the "debate with himself," criticizing Kerry for waffling on the issues. Stanzel said Mr. Bush will debate Kerry at the "appropriate time," but wouldn't say if that will be anytime soon.
Kerry's campaign is pinpointing six battleground states to debate issues where it says the Bush administration has been unsuccessful: homeland security and veterans in Pennsylvania, education in Arizona, the environment in Washington state, jobs and the economy in Ohio, health care in Missouri, and equal opportunity in Florida.
Kerry challenged Mr. Bush to monthly debates in mid-March, saying then that "America shouldn't have to put up with eight months of sniping."
Since Kerry emerged as the presumptive Democratic nominee, both candidates have criticized each other, at times sharply, on everything from national security to taxes. Kerry's first negative television ad, released Thursday, claims Mr. Bush's economic policies have shipped U.S. jobs overseas.
Regardless of whether the candidates agree to meet early in the race, a series of presidential debates is still scheduled for the fall, with an independent commission controlling the schedule.
Also Thursday, in what turned out to be an April Fool's joke, the Kerry campaign issued a press release that claimed a deal had been struck with Republicans for six debates.
Kerry Spokesman Jano Cabrera said he issued the release "in the spirit of the holiday."
The release noted at the end that April first would go down "as a historic day in presidential politics."
Cabrera later issued an apology for the release, noting that while it was a hoax, it did deal with the serious issue of whether President Bush would accept John Kerry's challenge to a series of debates before Election Day.
Kerry, meanwhile, was recovering off the campaign trail Thursday from minor shoulder surgery that his doctor described as free of complication.
The four-term Massachusetts senator underwent the 45-minute procedure Wednesday to repair tendons in his right shoulder and bicep. Dr. Bertram Zarins, chief of sports medicine at Massachusetts General Hospital, said Kerry would be in pain for a few days and probably need an ice pack and narcotic painkillers.
Kerry had no public schedule for the rest of the week.
Zarins said the presumed Democratic nominee was smiling and talking shortly after coming out of surgery.
"He joked a little bit and said, 'I hope I didn't reveal any state secrets,'" Zarins told reporters in a conference call.
The doctor also said Kerry would have to forgo temporarily the most time-honored tradition in politics: shaking hands.