Giffords, who co-founded a gun safety group with her husband, Mark Kelly, said in a statement Friday she was thrilled that her former House colleagues were responding to a gun-violence epidemic that killed nearly 40,000 people in 2017.
The bill expanding background checks "marks a critical first step toward strengthening America's gun laws and making our country a safer place to live, work, study, worship and play," Giffords said. "I stand ready to do everything in my power to get this legislation across the finish line."
Democrats promised swift action on gun control after the party regained the House majority following eight years of Republican rule. Pelosi called the bill on background checks a common-sense measure and cited polls showing 97 percent of Americans support background checks for all gun sales.
"Our Democratic majority will press relentlessly for bipartisan progress to end the epidemic of gun violence on our streets, in our schools and in our places of worship," Pelosi said. "Enough is enough."
Rep. Mike Thompson, D-Calif., who leads a gun violence prevention task force in the House, said he and other lawmakers from both parties have been pushing years to expand background checks and approve other gun-related bills, but have been stymied by Republican leaders.
Noting that many freshman Democrats ran on the issue of preventing gun violence, Thompson said political momentum to address gun violence is growing. "The American people have been demanding we take action and this new Congress will deliver," he said.
The background checks measure is likely to face opposition from the Republican-controlled Senate and the White House, where President Donald Trump has promised to "protect the Second Amendment." Jennifer Baker, a spokeswoman for the National Rifle Association, said a federal background check did not prevent Giffords' shooting, adding that "so-called universal background checks will never be universal because criminals do not comply with the law."
Lawmakers should "deal with the root cause of violent crime" instead of trying to "score political points and push ineffective legislation that doesn't stop criminals from committing crimes," Baker said.
The Trump administration moved last month to ban bump stocks, the firearm attachments that allow semi-automatic weapons to fire like machine guns. Bump stocks became a focal point of the gun control debate after they were used in October 2017 by a gunman in Las Vegas who fired into a crowd at a country music concert, killing 58 people and injuring hundreds more.
A new regulation gives gun owners until late March to turn in or destroy the devices.