The commercial is an unambiguous appeal to gun owners: a middle-aged hunter, shotgun in hand, vows that he will fight to protect the Second Amendment. But in a sensible, father-of-the-house tone, he also urges voters to support comprehensive background checks, “so criminals and the dangerously mentally ill can’t buy guns.”

The man behind the advertisement is not known for his kinship with the gun crowd: Mayor Michael R. Bloomberg, the nation’s fiercest advocate of restrictions on firearms since the December rampage at Sandy Hook Elementary School in Newtown, Conn.

Determined to persuade Congress to act in response to that shooting, Mr. Bloomberg on Monday will begin bankrolling a $12 million national advertising campaign that focuses on senators who he believes might be persuaded to support a pending package of federal regulations to curb gun violence. The ads, in 13 states, will blanket those senators’ districts during an Easter Congressional recess that is to be followed by debate over the legislation.

In a telling sign of how much the white-hot demands for gun control have been tempered by political reality, Mr. Bloomberg’s commercials make no mention of an assault weapons ban once sought by the White House and its allies, instead focusing on the more achievable goal of universal background checks.