That number is up from 2 million in November and is a 49 percent increase over December 2011, which saw 1.9 million background checks, the FBI's National Instant Criminal Background Check System said in a report cited by Politico Wednesday.
The background check program began in 1998 as part of the Brady Handgun Violence Prevention Act, Fox News said.
Since the Sandy Hook Elementary School shooting on Dec. 14 in Newtown, Conn., lawmakers across the country have called for tighter gun control. Sen. Dianne Feinstein, D-Calif., asked for an assault-weapon ban, and President Barack Obama said he's prepared to back such measures.
"I'd like to get it done in the first year," the president told NBC News, referring to the passage of tighter gun-control laws.
Adam Lanza, 20, used a semi-automatic rifle and a handgun in the Newtown incident in which he shot his mother to death in their home before killing 20 students and six adults at the elementary school. He killed himself with a handgun as police entered the school.