Mr Kerry expressed outrage after Mr Bush’s statement in an interview with Fox News, in which he was asked if he would still have shown up in a flight suit for that 2003 speech aboard an aircraft carrier.
“Absolutely,” Mr Bush was quoted as saying in excerpts of the interview, which is to air this week.
Mr Kerry, arriving in Madison, Wisconsin for debate preparations, called the statement “unbelievable”.
“I will never be a president who just says mission accomplished. I will get the mission accomplished,” said the Massachusetts senator. “That’s the difference.”
When Mr Bush gave his dramatic speech on May 1 last year, fewer than 150 Americans had been killed in the Iraq war. Since then the US death toll has risen to 1,046.
Mr Bush did not use the phrase “Mission Accomplished”, but that message was emblazoned on a prominent banner directly behind the president as he declared major combat operations over in Iraq.
Mr Bush’s interview aired for the first of a three-day run yesterday, just before he and Mr Kerry face off in their first televised debate on Thursday.
The 90-minute face-off in Coral Gables, Florida, will be the first of three presidential debates in the run-up to the November 2 election. The focus will be on foreign policy and many analysts think it is Mr Kerry’s best chance to try to overtake Mr Bush, who leads slightly in the polls.
Mr Bush held a mock debate on Saturday night with Republican senator Judd Gregg playing the role of Mr Kerry. Like Mr Kerry, the senator, who hails from New Hampshire, is a New Englander.
Mr Kerry’s aides gave only sparse details of the candidate’s debate preparations, although Ms Cutter said he had done at least one run-through with lawyer Greg Craig.
Mr Craig was White House special counsel during former President Bill Clinton’s impeachment.
The Bush team was eager to manage expectations. White House communications director Dan Bartlett talked up Mr Kerry’s experience but said Mr Bush would “hold his own”.