(CNN) – Michael Bloomberg's quest to enact stricter gun control measures continued Wednesday with a request from the billionaire New York City mayor to top Democratic donors: Stop supporting Senate incumbents who voted against a measure in April that would have bolstered background check requirements on gun sales.
Those Democratic senators – Mark Begich of Alaska, Heidi Heitkamp of North Dakota, Mark Pryor of Arkansas and Max Baucus of Montana (who's not running for re-election) – "sided with a gun lobby increasingly out of touch with Americans' priorities," Bloomberg wrote in his letter.
"I am writing to ask you: the next time these four Senators want you to support them with donations to their campaigns, tell them you cannot," Bloomberg continued. "Until they show that they will stand up for the American people and not the gun lobby, tell them you cannot support their candidacy."
The bipartisan measure that would have extended background checks to internet sales and gun shows failed to gain Senate approval in April. Its failure to pass was considered a major blow to gun control legislation that was pushed in the aftermath of the Sandy Hook Elementary School shooting in December.
Bloomberg's group Mayors Against Illegal Guns, along with other organizations pushing for tighter restrictions on firearms, pushed back against senators who voted "no" on the measure, including spending millions airing ads against both Democrats and Republicans.
Pryor, who's considered one of the most vulnerable incumbents up for re-election in 2014, defended himself in his own television spot, saying "No one in Washington tells me what to do. I listen to Arkansas."
The effect of Bloomberg's assault on pro-gun Democrats is not yet completely clear - some wonder whether the socially liberal mayor will actually help Democrats running for re-election in red states by attacking their positions on guns.
One statewide columnist in Arkansas, Steve Barnes, pointed to Bloomberg's support of abortion rights, gay marriage and stem cell research as potentially turning off voters in the state, though he submitted that Bloomberg also helped erase New York's $6 billion deficit. Bloomberg’s efforts to raise the cigarette tax and ban large soda drinks may also play against him in Arkansas, Barnes wrote.
“I still submit the Bloomberg ads may help Pryor more than hurt him,” he wrote.
Reached Wednesday, spokesmen for Heitkamp – who was elected to the Senate in November - and Pryor declined to comment on Bloomberg's attempt to shut off fundraising. A Begich spokesman didn't return calls requesting a response.
A Baucus spokesman told CNN that campaign contributions wouldn't influence the Montana senator's future votes.
Bloomberg's letter to donors was first reported by the New York Times.
Asked why Bloomberg was going after only Democrats, John Fleinblatt, a chief policy adviser to the mayor, said on a conference call Wednesday, "These aren't either or choices."
He said Mayors Against Illegal Guns will continue its advertising blitz, and is launching a national bus tour beginning Friday in Newtown, Connecticut, called "No More Names: The National Drive to Reduce Gun Violence" marking the 6 month anniversary of the school shooting there.
"All of these are part of the process to urge Congress to take a second look at this matter," Fleinblatt said on the call.
When asked if the group would do more ads targeting Democrats who voted against the background checks measure, one official with the group said "stay tuned."
CNN's Kevin Bohn and Todd Sperry contributed to this report.