"What we've got to do first is try to do everything we can to help Joe Biden," Bloomberg said in a news conference in New York. "We sent some of the people down to Washington, and we had some people on the phone to give Joe Biden our ideas."
Bloomberg, who plans an advertising campaign for stricter gun-control laws featuring Hollywood stars, told reporters he wanted to see criminal background checks on all gun sales, not just at gun dealers.
He said he also sought better enforcement of existing checks.
"The whole thing takes about 90 seconds," CNN quoted Bloomberg as saying Monday. "You type in the name, you hit the 'Go' button and bang, back it comes and says 'yes' or 'no.'
"Costs next to nothing," he said. "It would be very easy for private transactions."
Bloomberg, a political independent who vows to spend millions of dollars over the next two years to aid political candidates willing to oppose the gun lobby, called for the creation of a federal assault weapons ban similar to the Public Safety and Recreational Firearms Use Protection Act passed by Congress Sept. 13, 1994.
That law expired 10 years later.
Bloomberg said Biden was a leading senator in the 1994 law's creation.
"I think all of us know that Joe Biden is not a shrinking violet, particularly when it comes to crime and the gun problem in this country and the number of murders," Bloomberg said.
President Barack Obama appointed Biden Dec. 19 to lead an effort that would result in recommendations to prevent another mass shooting like the Dec. 14 Sandy Hook Elementary School shootings in Newtown, Conn., which left 20 children and six adult staff members dead and two others wounded.
Obama gave the group a deadline of "no later than January" to propose new laws and actions "that I then intend to push without delay."
The Washington Post reported Sunday the White House was working on a far broader and more inclusive approach to curbing gun violence than reinstating the 1994 ban on assault weapons and high-capacity ammunition.
The working group is considering measures that would require universal background checks for firearm buyers, track the movement and sale of weapons through a national database, toughen mental health checks and increase penalties for carrying guns near schools or giving them to minors, the newspaper said, citing multiple people involved in the discussions.
To promote such changes, the White House is considering ways of working around the National Rifle Association that one source told the Post could include seeking support from Walmart and other gun retailers for measures that would benefit their businesses.
The NRA is lobbying for a plan that would equip every school with an armed guard.