President Barack Obama appointed Biden to head a task force to make recommendations on reducing gun violence in the United States, following the Dec. 14 massacre at Sandy Hook Elementary School in Newtown, Conn., in which 20 first-graders and six adults were shot to death.
Biden said he hopes to have recommendations ready by Tuesday.
"We know that there is no silver bullet," Biden said after his meeting with representatives of the video games industry Friday. "We know this is a complex problem."
The National Rifle Association Thursday accused the White House of having "an agenda to attack the Second Amendment" and vowed to lobby Congress to stop U.S. gun limits.
Biden said he thought his meeting with NRA representatives was "very straightforward, productive" but refused to comment on the NRA statement.
Biden has met with entertainment industry representatives and plans to meet with technology experts to discuss such proposals as making it impossible for anyone to fire a gun except the "person who purchased it."
Biden said there is growing support for tighter background checks on gun purchasers, restrictions on high-capacity clips and other moves.
The New York Times reported Friday the White House believes a ban on military-style assault weapons will be exceedingly difficult to get through Congress. So it is pressing for other gun rules it thinks are more likely to win bipartisan support and reduce gun deaths.
The White House doesn't want to make passing an assault-weapons ban the only definition of success, the Times said.
One option the administration is considering, the Times said, is toughening laws against people who buy firearms for others, a practice known as a "straw purchase," where the buyer lies about the identity of the ultimate possessor of the weapon. The administration is considering longer prison terms for those who buy guns for others, the newspaper said.
Some administration officials discussed expanding mandatory minimum sentences for gun law violations, but the White House doesn't generally like that idea, the Times said.
Biden's task force -- which includes Attorney General Eric Holder, Homeland Security Secretary Janet Napolitano and other Cabinet officials -- is also considering seeking additional money to enforce existing laws, the Times said.
After Thursday's meeting with the task force, the NRA issued a statement, assailing the administration.
"We were disappointed with how little this meeting had to do with keeping our children safe and how much it had to do with an agenda to attack the Second Amendment," the statement said.
"We will not allow law-abiding gun owners to be blamed for the acts of criminals and madmen," the statement said. "Instead, we will now take our commitment and meaningful contributions to members of Congress of both parties who are interested in having an honest conversation about what works -- and what does not."
Biden's task force has met with a number of groups this week, including medical associations, victims' rights and sportsmen's groups, entertainment-industry trade groups and gun retailers.
The video game industry has been criticized, especially after the Newtown killings, for selling first-person shooter games, such as "Call of Duty" and "Medal of Honor: Warfighter," The Hill said.
Lawmakers and the NRA have suggested violent video games contribute to real-life aggressive behavior.
Sen. Jay Rockefeller, D-W.Va., introduced a bill last month that would require the National Academy of Sciences to study the effects of violent video games and video programming on children, The Hill said.