Suffolk District Attorney Daniel F. Conley has entered the national gun-control fray, criticizing US Senate minority leader Mitch McConnell for saying he would be willing to block debate on a measure to expand background checks on gun buyers.

Conley, who launched a bid for mayor of Boston last week, singled out the Republican senator from Kentucky on Tuesday in a letter urging him to “stop playing games” and allow a vote on the bill. McConnell has said that he would join a group of 13 other Republican senators to filibuster a gun control bill that Democrats plan to bring to the Senate floor Thursday.

“Senator McConnell, I implore you and your allies in the Senate to stop obstructing legislation that nearly every American is demanding,” Conley said in the letter. “Listen to your fellow Republicans who rightly recognize that this matter should come to a vote.”

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Conley, who took office as district attorney in 2002, said that during his tenure illegal guns have accounted for more deaths in Suffolk County than all other weapons combined. Ten people have been killed with illegal firearms since the deadly shooting at Sandy Hook Elementary School in Newtown, Conn., four months ago, which reignited a fierce national debate on gun control, he said.

“The tired response that background checks would not have prevented the massacre at Sandy Hook is a perversion of logic and an insult to the memory of the victims,” Conley said. “Background checks would unquestionably prevent someone with a long and violent history from legally purchasing a firearm.”

Two key brokers, Senators Joe Manchin III, a Democrat from West Virginia, and Pat Toomey, a Republican from Pennsylvania, reached a bipartisan deal on background checks that would expand coverage to all commercial gun sales, including at gun shows and online, but exempt private sales.

But if McConnell can muster 41 votes from within his party’s ranks — or wrestle several moderate Democrats to his side — he could prevent supporters of the proposed gun control bill from rallying the 60 votes needed to block a filibuster in the Senate.

Conley, who for years has fought for tougher gun laws, said in his letter that more than 80 percent of guns used to commit crimes in the Commonwealth come from other jurisdictions, a problem he said the state has tried to remedy despite federal obstruction.

“Over the years, we in Massachusetts have enacted and updated any number of laws to address this critical public safety issue, but those laws are too often undercut by lax federal regulations,” he said. “When a violent offender can purchase a killing tool with no background check in any number of neighboring states, the result is low-cost and easily available weaponry on our city’s streets.”