Democrats’ recent shift on gun control politics is getting a new test run this year in the Virginia governor’s race, where Lt. Gov. Ralph Northam on Tuesday won the endorsement of former Rep. Gabrielle Giffords’ gun control group, while Republican Ed Gillespie is embracing his own support from the National Rifle Association.

Mr. Northam, a Democrat, said it was a “tremendous honor” to receive the endorsement from the political arm of Americans for Responsible Solutions, which was co-founded by Ms. Giffords and her husband Mark Kelly in 2013.

“I’m not at all ashamed of having an ‘F’ rating from the NRA,” Mr. Northam said on a conference call Tuesday. “I will continue to stand up against their motives.”

Mr. Kelly said too many elected leaders are “caught in the grips” of the gun lobby but that Mr. Northam is ready to fight for items like increased background checks and stronger trafficking laws.

“We need leaders like Ralph Northam who are willing to run on this issue, and who aren’t afraid to work across the aisle to save people’s lives,” he said.

In addition to the support from Ms. Giffords’ group on Tuesday, Mr. Northam has also won the backing of Everytown for Gun Safety, the gun control group founded in part by former New York City Mayor Michael Bloomberg in 2014.

Mr. Northam’s embrace of gun control is the continuation of a major shift for the state’s Democrats, who used to take a much less strident approach to Second Amendment issues, hoping to win rural voters for whom hunting is still a culture.

Mr. Gillespie is hoping to capitalize on that. “As governor, Ed will protect Virginians’ individual rights under the Second Amendment. Ralph Northam will not,” said Gillespie campaign spokesman David Abrams.

The NRA also hit back at Mr. Northam on Tuesday, saying he’s being endorsed by out-of-state groups because he supports the same “extreme gun control agenda” pushed by Mr. Bloomberg and former President Barack Obama.

“A vote for Ralph Northam is a vote to extend the McAuliffe era of hostility toward law-abiding gun owners,” said NRA spokesperson Catherine Mortensen, referring to current Democratic Gov. Terry McAuliffe.

Little more than a decade ago, Democratic politician Mark R. Warner courted the NRA’s support when he ran for governor in 2001. The NRA ultimately declined to endorse a candidate in the general election, which some analysts said helped Mr. Warner build support in the state’s southwest and win a fairly close race.

But by 2013 Mr. McAuliffe wasn’t doing anything to try to hide his “F” NRA rating in that year’s race against Republican Kenneth T. Cuccinelli II.

Gun control activists point to Mr. McAuliffe’s win as evidence that a Democrat doesn’t need to tack right on the issue anymore to win statewide in Virginia, which has also been a key battleground in the past few presidential election cycles.

“Gun safety wins at the ballot box, particularly here in the NRA’s backyard,” John Feinblatt, president of Everytown, said in endorsing Mr. Northam and several other Democratic candidates earlier this year.

But Philip Van Cleave, president of the Virginia Citizens Defense League, said that sort of analysis is off, pointing to Mr. McAuliffe’s narrow margin of victory in 2013 and more recent victories at the national level for Republicans in 2016.

“No, it’s not working for them,” he said. “They’re squeaking in because they’re getting lots and lots of money. That’s not the hearts and minds of people.”

“We got a Republican president, a Republican House and a Republican Senate,” he said. “Is that a working message?”

Mr. Warner, after courting the NRA as governor, would later anger the group by voting in the U.S. Senate to expand gun-purchase background checks in 2013. He won re-election in 2014 over Mr. Gillespie despite the GOP candidate having the NRA endorsement that time.

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