While New York City Mayor Michael Bloomberg said two months ago he was determined to fight for a ban on assault weapons, the outspoken gun critic said Monday he's concentrated on another legislative proposal.

"Our focus is on background checks," he said on CNN's "The Lead with Jake Tapper."

Bloomberg was confirming reports that Sen. John McCain had said the mayor was focusing on background checks. The two met last month.

In the interview, the mayor also elaborated on why he's spending his own money in the gun debate, and whether he plans to continue spreading his cash after his third term ends in 2014.

Talking about gun control, Bloomberg pointed to statistics showing the vast majority of gun deaths, including suicides, in the United States come from hand guns, not assault weapons.

"This year in America, 12,000 people will be killed with handguns. Four hundred people will be killed with assault weapons or high capacity magazines," he said. "So it is the vast bulk of - of the, uh, murders are done with handguns."

Lawmakers in Washington have floated a number of proposals to combat gun violence since the Connecticut elementary school shooting in December that killed 20 children and six adults. Of those proposals, a push to strengthen the background check system has proved to be the most likely to get through Congress.

The Senate Judiciary Committee approved a bill last week that would expand background checks covering all U.S. firearms sales, including private transactions by non-licensed sellers. The bill now goes to a full vote in the Senate.

It also approved a new ban on semiautomatic firearms modeled after military assault weapons. The bill, however, has little chance of becoming law due to fierce opposition by the National Rifle Association and a certain GOP filibuster.

In January, Bloomberg acknowledged that a ban on assault weapons would be "a tougher sell" but said he was nevertheless "optimistic."

"There are lives involved here. And if you can save one life, isn't that worth trying?" Bloomberg said two months ago on CNN's "Anderson Cooper 360."

The mayor on Monday reiterated his concern about those types of guns, saying they still need to be kept out of the hands of non-military gun owners.

"They don't belong in the home and they don't belong in big cities. They're weapons of war," he said on "The Lead." "They're designed to kill people, not to protect anybody."

However, he was also ready to emphasize a need for a more robust background check system.

"The 14 states that have taken on the burden of also having background checks for gun shows and for internet sales, they reduced their suicide rate by 50 percent," he said. "So gun background checks really do work."

Mayors Against Illegal Guns, a group co-chaired by Bloomberg, has had an active role in the recent gun debate. The group has purchased air time for ads and held events on Capitol Hill urging lawmakers to take action on the issue.

Bloomberg's super PAC, Independence USA, spent $2 million in the recent Democratic primary for the Illinois special election to fill Rep. Jesse Jackson Jr.'s seat. The group successfully backed state Rep. Robin Kelly over former U.S. Rep. Debbie Halvorson, who opposed an assault weapons ban.

Asked if his efforts to influence political races were similar to actions taken by Charles and David Koch--the billionaire brothers who've been much maligned by opponents for injecting their wealth into the political scene--Bloomberg said he has no problem with what they're doing.

He added he knows David Koch well and argued Koch is simply tying to help "get the policies that he thinks would be better for society."

"He's using his own money. I have no problems with what he's doing. And I'm sure he wouldn't have any problems with what I've done," he said.

As for what the mayor will do next, he said: "I guess go out and look for a job."

"I work cheap," he said. "I get paid a dollar a year now. So, uh, the salary is not going to be the problem."