Biden helped write the 1994 Violent Crime Control and Law Enforcement Act, which included an assault-weapons ban that expired in 2004.
Biden said the administration will need the help of law enforcement to get the ban reinstated.
Sen. Dianne Feinstein, D-Calif., and other lawmakers have said they will introduce legislation banning assault weapons when the new Congress convenes in January.
Obama reiterated his support Wednesday for the Second Amendment, which guarantees the right to bear arms, but said, "We should be able to keep an irresponsible, law-breaking few from buying a weapon of war.
"There is a big chunk of space between what the Second Amendment means and having no rules at all. And that space is what Joe is going to be working on to try to identify where we can find some common ground," Obama said.
Obama promised to use "all the powers" of his office to overcome deep-seated political resistance to gun control.
The Wall Street Journal said those powers would likely include using administrative action to put some gun regulations into place.