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Despite President Bush's call to stop airing television ads blasting John Kerry's (search) war record, a spokesman for a group of Vietnam veterans said Tuesday it would continue its controversial campaign.

"We're not going to stop. We'd be doing this if John Kerry was a Republican," Van Odell (search), a Vietnam veteran and one of the leaders of Swift Boat Veterans for Truth (search), told "FOX and Friends."

Odell said he and others in the group were exercising their free speech rights. "I don't know how freedom of speech could be bad for the system," Odell said. "We paid for that through our blood and service in Vietnam."

On Monday, Bush said ads from Swift Boat Veterans for Truth, an unregulated 527 group, should be pulled.

"That means that ad and every other ad. I don't believe we ought to have 527s. I think they're bad for the system," Bush said on Monday in Crawford, Texas, in reference to the groups named after their status in the tax code. "I frankly thought we'd gotten rid of it when I signed McCain-Feingold" campaign finance reform.

Bush said that he thought Kerry "served admirably and he ought to be proud of his record," but it didn't seem likely on Tuesday that the president's remarks would extinguish the political firefight that has mounted over Kerry's service in Vietnam.

Both sides said they wanted to focus on the issues, not Vietnam.

"We're focused on the issues of today, not 35 years ago," said Republican National Committee Chairman (search) Ed Gillespie.

But speaking at Cooper-Union University in New York City on Tuesday, Kerry alleged the Republican camp is trying to keep the focus on Kerry's service to divert from its own record.

"The Bush camp has turned to a calculated campaign of smear and fear because they can't talk about jobs, health care, energy independence and rebuilding our alliances," he told a supportive crowd.

Early in the day, former Democratic candidate Howard Dean (search) said that Bush "broke the law" by having a member of his veterans advisory panel appear in an ad attacking Kerry. Dean said the veteran who appeared in the second Swift boat ad, Ken Cordier, was "part of the Bush campaign," even though the White House has described him as a volunteer member of a panel on veterans policy unconnected to the president's campaign.

Dean said Bush should "apologize" to the country for the attack ad and breaking the law.

Former Michigan Democratic Sen. Don Riegle told FOX News that the ad campaign is "sleazy" and "disgusting."

"Bush ought to stand up and tell them to put a stop to it. The Bush crowd and the Bush operatives have their fingerprints all over this thing."

In a reference to Bush and Cheney's actions during the Vietnam War, Riegle said, "The problem here is Bush and Cheney want to be tough guys, but when they had a chance to be tough guys in real life they didn't do it."

But former Rep. Dan Lungren, R-Calif., said that Kerry is the one who brought up the Vietnam War, and the president has not made an issue of Kerry's war record because he's "trying to make an issue of John Kerry's particular record in the Senate, which I think is a record that once examined would result in people deciding not to vote for him for president."

Kerry senior adviser Michael Meehan told FOX News that Bush didn't do what Kerry implored because he didn't denounce the Swift boat ads specifically, but called for an end to all 527 ads.

The uproar over Kerry's service has dominated much of the political news since the Democratic senator from Massachusetts accepted his party's presidential nomination with a speech that centered on his biography and his military service.

Kerry spent four months in Vietnam leading a "swift boat" crew but was sent home after accumulating his third Purple Heart for injuries he received.

"Swift boat" was the common term in Vietnam for the small U.S. Navy patrol boat officially known as a Patrol Craft Fast (search), or PCF.

The political attacks on Kerry have been twofold. First, critics say Kerry embellished his Vietnam record. Second, they say Kerry disrespected his fellow veterans when he returned home and testified before Congress about what he described as "atrocities" being committed by Americans in combat.

Questions have arisen surrounding one of his Purple Hearts (search), which was awarded for injuries suffered on Dec. 2, 1968. Nine days later, Kerry wrote in his journal that he and his crew "hadn't been shot at yet." This passage of Kerry's diary was reprinted in Douglas Brinkley's book "Tour of Duty."

A senior Kerry official told FOX News on Monday that there had been a "couple of instances" where the Kerry journal entries in Brinkley's book were misdated, but added that no specific evidence indicated that they had been misdated in this case.

Asked earlier this month about whether the wound may have been unintentionally self-inflicted, Kerry defender and National Director of Veterans for Kerry (search) John Hurley said: "Anything is possible, but what you have to remember is that John Kerry that night was on a small boat, a 14 to 15 foot Boston whaler, with two other men, going into an inlet where intelligence had told them the VC was using as a crossing, trafficking in contraband. They went in there; they saw VC; they popped a flare; they took them under fire. At some point John Kerry felt a stinging burning sensation in his arm, and was injured."

He added that the only men who would know for sure what happened were the three men on that operation — Kerry, Pat Runyan and Bill Zeladonous.

Hurley attacked the Swift Boat Vets' ads as "dishonest and dishonorable."

"This is a Republican smear campaign. ... The United States Navy awarded John Kerry a Silver Star, a Bronze Star and three Purple Hearts. Every single man who served under his command, when he won those awards, supports John Kerry," Hurley told "FOX News Sunday," adding that all the members of the Swift Boat group except for one never met Kerry in Vietnam.

That one sailor was Van Odell.

"We're not a political party," Odell said Tuesday. "We're trying to bring out the truth of what actually happened in Vietnam."

FOX News' Steve Centanni, Major Garrett and Sharon Kehnemui contributed to this report.