“One of the first things you want to do is close the gun-show loophole,” said Mr. Leahy, in an interview for C-SPAN’s “Newsmakers,” referring to a legal provision that permits unlicensed gun sellers to sell to people without conducting background checks. The loophole is a small piece of a much broader agenda introduced by Mr. Obama on Wednesday, one that faces considerable, though not insurmountable, odds on Capitol Hill.

The view of Mr. Leahy, a Democrat with a history of supporting some gun rights, is crucial because the work of his Judiciary Committee will be central to advancing any new gun legislation.

He declined to detail precisely how the committee, which will hold hearings on potential gun legislation this month, would proceed with Mr. Obama’s request to push legislation that includes a renewal of an assault weapons ban, a limit on magazine size and universal background checks.