New York Mayor funds $12m gun law campaign
NRA chief executive, Wayne LaPierre, said Mr Bloomberg was "going to find out this is a country of the people, by the people, and for the people".
"And he can't can't spend enough of his $27bn to try to impose his will on the American public," Mr LaPierre told NBC television's meet-the-press on Sunday.
Mr Bloomberg told the same NBC programme that opinion polls showed there was overwhelming public support for tighter background checks.
"We are trying to do everything we can to impress upon senators that this is what the survivors want and this is what the public wants," he said.
Congress is due next month to consider legislation drafted by the Obama administration in response to last December's shooting at a school in Newtown, Connecticut, that killed 20 children and six adults.
President Obama had been seeking a ban on military-style assault weapons, but this was dropped from the bill last week when it became clear it would not find sufficient support in the Republican-led House of Representatives.
Instead, gun control advocates are now focusing on another of Mr Obama's proposals — to implement wider background checks on people purchasing firearms.
Currently, around 40 per cent of gun sales — among them those conducted at local gun shows — are exempt from such checks, BBC report said.
Gun control is a particular issue in the 13 states being targeted by the television advert this week.
Both sides believe the next few weeks —when members of Congress are in their homes states during Easter recess - could be crucial to the gun control debate, our correspondent says.
The NRA is planning its own advertising campaign, but despite being one of the best-funded lobby groups in America, its spending is unlikely, for the moment at least, to rival that of Mr Bloomberg, he said. — BBC