Burr is locked in a tight race for a third term against Deborah Ross, whom national Democrats see as one of their best chances to pick up a seat as they try to retake the Senate. Burr is the chairman of the Senate intelligence committee and one of the chamber's more powerful Republicans.
Ross, who has hammered Burr for supporting Donald Trump, said the remark was out of line. Trump ignited his own controversy on the subject in August when he suggested "Second Amendment people" might find a way to stop Clinton from rolling back gun rights with her Supreme Court nominations. Trump later said he was merely trying to suggest the strong voting power of gun rights supporters.
On the audio obtained by CNN, Burr tells a private gathering about his thoughts when he saw a copy of American Rifleman in a gun shop.
"It's got a picture of Hillary Clinton on the front of it. I was a little bit shocked that it didn't have a bull's-eye on it," Burr said on the recording CNN said was made Saturday in Mooresville, about 30 miles north of Charlotte.
Burr issued a statement of apology Monday afternoon shortly after CNN published the recording: "The comment I made was inappropriate, and I apologize for it."
Ross said the remark was "not befitting a senator."
"I think it's a comment about violence against a candidate for the president of the United States, and they're irresponsible and wrong," Ross said in a telephone interview Tuesday.
Burr's comments normalize an attitude among some gun rights supporters that killing unfriendly politicians could be an option, Brady Campaign President Daniel Gross said Tuesday. The group advocates for gun control legislation and is named for James Brady, the Ronald Reagan aide wounded in an attempt to assassinate the president in 1981.
"We take from it a level of violent rhetoric that is dangerous and we need to say is unacceptable," Gross said in a telephone interview.
A Burr spokesman did not respond to a request for further comment Tuesday. But the state Republican Party lashed out, with Executive Director Dallas Woodhouse repeating attacks on Ross for her work for the state chapter of the American Civil Liberties Union and Clinton's email scandal.
The audio obtained by CNN also captured Burr joining a handful of GOP senators who have said they would continue blocking nominees to the U.S. Supreme Court if Clinton is elected.
"If Hillary Clinton becomes president, I am going to do everything I can do to make sure four years from now, we still got an opening on the Supreme Court," Burr said.
Texas Sen. Ted Cruz and Arizona Sen. John McCain have also said the GOP will block any Democratic nominee to replace the late Justice Antonin Scalia, who died in February. President Barack Obama nominated Judge Merrick Garland for Scalia's seat in March. Senate Republicans declined to even hold hearings, insisting voters choosing the next president would have the final say.
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