Boston ? John Kerry fought back Thursday against campaign allegations that he exaggerated his combat record in Vietnam, accusing President Bush of using a Republican front group “to do his dirty work” and challenging Bush to debate their service records.

“Well, if he wants to have a debate about our service in Vietnam, here is my answer: Bring it on,” said the Democratic presidential candidate, reviving an old war and campaign slogan amid strong urging from party leaders for him to respond to 2-week-old GOP assertions.

A campaign ad for Democratic presidential nominee Sen. John Kerry, D-Mass., released shows Jim Rassmann a veteran who served with John Kerry in Vietnam, and, pictured, Kerry in Vietnam. Kerry's campaign rolled out the ad Thursday to counter a spot that claims Kerry lied about his war record.

As Kerry denounced the criticism as “lies about my record,” aides privately acknowledged that they and their boss had been slow to recognize the damage being done to his political standing.

Kerry won three Purple Hearts, a Bronze Star and Silver Star for Vietnam War combat. Bush served stateside in the Texas Air National Guard. Both men say the other served honorably, but their supporters are pouring thousands of dollars into television ads and other tactics to insist otherwise.

MoveOn.org, a liberal group funded by Kerry supporters, is airing an ad accusing Bush of using family connections to avoid the Vietnam War. It also asks the president to denounce an ad that aired early this month by “Swift Boat Veterans for Truth,” a GOP-leaning group of Vietnam veterans who say Kerry exaggerated his actions to win Vietnam War medals.

Bush campaign spokesman Steve Schmidt said the charge that Bush was in league with the group criticizing Kerry’s war record was “absolutely and completely false. The Bush campaign has never and will never question John Kerry’s service in Vietnam.”

Knowing several news organizations were investigating the claims of anti-Kerry veterans, the Democratic campaign swung into action late Wednesday — rewriting the candidate’s speech to a firefighters union overnight, and producing a new campaign commercial, despite earlier plans to stay off the air until September.

The 30-second ad features a former Green Beret saying Kerry saved his life under fire. “He risked his life to save mine,” Jim Rassmann says.