Biden said he has not finalized his recommendations, but a consensus was emerging over banning assault weapons and high-capacity ammunition magazines and tightening background checks.
Some of the proposals faced opposition by pro-gun groups - most notably the National Rifle Association. A representative from the NRA met with the vice president Thursday afternoon.
The NRA rejected the effort to limit ammunition and dug in on its opposition to an assault weapons ban.
The NRA has said it does not think there should be any new gun laws and that the U.S. should enforce the current ones.
White House officials recognize it is unlikely the NRA will ever fully support measures the Obama administration is pushing.
The vice president, who is leading an administration-wide review of gun safety laws, kicked off his gun violence task force Wednesday in Washington. He met with gun safety groups and those who have survived gun violence.
The effort was spurred by last month's mass shooting at Sandy Hook Elementary School, where 20 children and six adults were killed.
Biden also met Thursday with sportsmen's and wildlife interest groups, as well as with representatives from the entertainment industry.
The vice president will be presenting President Barack Obama with recommendations for curbing gun violence. His deadline has been set for late January.
The Associated Press contributed to this report.