President Bush (search) said Monday that a veterans' group should stop airing television ads criticizing John Kerry's (search) war record.

Bush said ads from Swift Boat Veterans for Truth (search), a 527 group named after its status in the tax code, should be pulled. The call from Bush could open him up to charges that the Bush-Cheney campaign is coordinating with an unregulated political organization.

"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. "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 remains undecided whether that will extinguish the political firefight that has built over Kerry's service in Vietnam.

Consider the latest:

— Former Sen. Bob Dole (search) — the Republicans' 1996 presidential nominee — suggested Sunday that Kerry apologize for past testimony before Congress about alleged atrocities during the Vietnam War. He joined critics of the Democratic presidential candidate who say he received an early exit from combat for "superficial wounds."

— On Monday, Democratic vice presidential candidate John Edwards said Bush should call for the group to remove the ad. He called Bush's decision to do so a "test of character" for the president. After Bush's comments, Edwards expressed disappointment.

"The moment of truth came and went, and the President still couldn't bring himself to do the right thing," he said. 

— Also on Monday, Democrats arranged for reporters a conference call with Navy swift boat officers Rich McCann, Jim Russell and Rich Baker, who said Kerry acted honorably and bravely. In a separate news conference in Harrisburg, Pa., crewmate Del Sandusky said he personally witnessed the battle action for which Kerry received Silver and Bronze stars and two of his three Purple Hearts.

"He deserved every one of his medals," Sandusky, a retired computer repairman who drove Kerry's boat for nearly three months.

— On Sunday, the Kerry campaign released a new ad accusing the president of backing Swift Boat Veterans for Truth (search), the group which has released a series of spots calling into question Kerry's heroism. In the Kerry ad, the narrator claims that families are losing jobs and health care while "George Bush's campaign supports a front group attacking John Kerry's military record." The ad calls the attacks "smears" and "lies."

— In response to the Kerry ad, the Bush campaign sent a letter to television station managers Monday "to set the record straight." The Bush campaign letter "flatly rejects this baseless allegation of illegal coordination between Bush-Cheney '04 and a group called Swiftboat Veterans for Truth."

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.

Kerry defender and National Director of Veterans for Kerry (search) John Hurley called the Swift Boat Vets' ads "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, Van Odell, a member of Swift Boat Veterans for Truth, said Kerry was not under enemy fire, as the "after-action report" that earned him his Bronze Star states.

"I do not have a document that says that," Odell admitted, adding that no one else at the scene of the fight thought it was medal-worthy. "I was up at the highest point. I could see all around. I could see what was going on. I fired a few hundred rounds when the mine first went off. And after that we quit firing because — and then we spent an hour in the kill zone, and nobody was shot or wounded.

"None of us knew that he even got the Bronze Star. None of us knew that any of this was going on. We didn't know until after he left about the Purple Heart. And I didn't know about his Bronze Star until about three months ago that they got for this action," he told FOX News Sunday.

Odell also rejected charges that the organization he represents is funded by people who have worked in conjunction with the Republican Party.

"Our message is our message, and no one tells us what to say," Odell said.

Federal law prohibits any direct involvement between private organizations, known as 527s, and anyone connected to a presidential campaign. On Sunday, the Bush campaign stated that it had released from volunteer duty a campaign worker who served in Vietnam and appears in one of the Swift Boat ads. The campaign said Col.Ken Cordier (search) failed to disclose his involvement with the group.

Democrats complain that the Republican Party's involvement goes much deeper than that.

The swift boat group clearly "is coordinated with the Bush Cheney campaign," said Angelo Genova, attorney for the Democratic Party. There is "direct evidence of overlapping consultants, overlapping fund-raisers. ... Here we have Texas supporters of the president involved. Karl Rove himself has been implicated."

Jan Baran, former general counsel for the Republican National Committee, dismissed these charges. "All of the factual allegations regarding overlap under FEC regulations are basically superficial."

All the back-and-forth is disappointing Sen. Joe Lieberman (search), D-Conn., the 2000 Democratic vice presidential candidate. He told FOX News Sunday that Kerry's war record has consumed all the attention while more important issues in the presidential campaign are being ignored.

"What really infuriates me and amazes me is that we're spending this much time and energy debating what happened 35 years ago instead of talking more about the war on terrorism we're in today, about our health care, education, environment, economic problems, and what George Bush and John Kerry are going to do for the next four years. That's what we ought to be debating."

Fox News' Steve Centanni and Sharon Kehnemui contributed to this report.