"I am for making sure that we increase the quality of information in the database that is in existence already," Cantor said.
President Obama and congressional Democrats have called for closing the gun show and Internet loopholes that allow for the sale of firearms without a background check.
"The vast majority of Americans, including a majority of gun owners, support requiring criminal background checks for anyone trying to buy a gun," Obama said Monday in Minneapolis, at an event with law enforcement officials.
A poll released last month by CNN showed that 94 percent of adults favored background checks for all gun purchases.
But the National Rifle Association has argued against the practice, saying that the expansion of background checks would place a burden on legal gun owners and be ignored by criminals.
“If I want to sell you a shotgun or something like that ... we'll have to go find a dealer or walk into a police station. Who's going to do the check? There's going to be fees. There's going to be paperwork. There's going to be law-abiding people caught up in a bureaucratic nightmare," NRA CEO Wayne LaPierre told Fox News last month.