The strategy will focus not on sweeping federal restrictions to ban certain weapons, but instead will seek to expand the background check system for gun buyers both at the state and national levels.

The $50 million could be significant: In recent years, the N.R.A. has spent only $20 million annually on political activities. The political groups affiliated with the billionaire Koch brothers, who are seeking to help Republicans take over the Senate, have spent about $30 million in the last six months.

The group will zero in on 15 target states, from places like Colorado and Washington State, where gun control initiatives have advanced recently, to territory that is likely to be more hostile like Texas, Montana and Indiana. They have set a goal of signing up one million new supporters this year on top of the 1.5 million they already have.

Previous efforts by Mr. Bloomberg to push gun control have touched off tensions with national Democratic leaders, because he has run negative ads against incumbent Democrats whom he views as insufficiently supportive of gun control. The Democratic leaders argue that Mr. Bloomberg threatens to hand control of the Senate to Republicans, which they say would doom any hope of passing gun control legislation.

Mr. Bloomberg dismissed those fears, saying he was concerned only with the long term.

“You can tell me all you want that the Republicans would be worse in the Senate than the Democrats,” he said. “Maybe they would. But that’s not what we’re talking about here.”

Underscoring his desire to work with both parties, Mr. Bloomberg is bringing on a new advisory board with prominent Republican and Democratic figures. Tom Ridge, the former Pennsylvania governor and Homeland Security secretary under President George W. Bush; Eli Broad, the philanthropist; Warren Buffett, the investor; and Michael G. Mullen, the former chairman of the Joint Chiefs of Staff under both Mr. Bush and President Obama, will all be board members.

Mr. Bloomberg acknowledged that his new efforts would require a dedication not just of money but also of time — two things he now has in abundance.