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A centrist organization and two other groups devoted to gun control are denouncing supporters of Senator Bernie Sanders who have been arguing that he has a “strong record against gun violence,” the latest salvo between backers of the Vermont senator and Hillary Clinton on the topic of firearms.

The letter from the group Third Way, which was also signed by officials with the Brady Campaign to Prevent Gun Violence and Americans for Responsible Solutions, the group co-founded by former Representative Gabrielle Giffords of Arizona, was sent this week to Democracy for America. The liberal grass-roots group has endorsed Mr. Sanders, and has sought to come to his aid as he has been criticized by Mrs. Clinton for his record on gun control.

“We, the undersigned, all lead groups who have been deeply involved in the cause of gun safety for many years, and we were taken aback by D.F.A.’s recent press release arguing that Senator Bernie Sanders has a ‘strong record against gun violence,'” officials with the groups wrote. They singled out Charles Chamberlain, the executive director for D.F.A., saying that anyone who “purports to be a progressive on this issue would conclude precisely the opposite.”

The Brady Campaign and Ms. Giffords have endorsed Mrs. Clinton, who has made gun control, an area where she has been to the left of Mr. Sanders, a central issue of her candidacy. The issue has taken on new urgency amid a string of mass shootings across the country.

The letter went on to say that there have been “two monumentally important votes in Congress on gun safety, and Senator Sanders was wrong on both of them.” One was in support of the so-called Brady Bill, which established the federal background checks system, and the other was a 2005 bill that gave gun manufacturers legal immunity. Last weekend, before the final Democratic primary debate before the Iowa caucuses, Mr. Sanders changed his position on that issue.

“These were the decisions that have really mattered,” they wrote.

Mr. Sanders has strongly defended himself against Mrs. Clinton on the issue of guns, noting that he has a D-minus rating from the National Rifle Association.

The letter from the three groups to Democracy for America argued that those ratings are based on a number of factors, not solely votes related directly to guns.

“We trust that with this new understanding of the gun safety record of Senator Sanders, coming from people who have fought for the progressive position in this debate, your organization will retract its mistaken characterization,” the officials with the groups wrote.

In an interview, Mr. Chamberlain described Third Way as “a Wall Street front group” and criticized it for an attack “on the purity of progressive issues.”

“I think it’s a little disappointing to see our friends at the Brady Campaign” being “misled” on the subject, said Mr. Chamberlain, noting that Mr. Sanders has repeatedly supported background checks.

“If that isn’t a clear, strong record on gun safety, then I don’t know what is,” he said.