WASHINGTON — Democratic leaders in Congress and the White House renewed their push for gun legislation on Thursday, just months after it was defeated in the Senate, amid delicate talks on a new background-check measure that advocates hope could change enough votes from no to yes.
But those negotiations met a warning from Senator Harry Reid of Nevada, the majority leader, who said he would not accept any bill that is substantially weaker than the one defeated in April.
“The bill that passes the Senate must have background checks, and not a watered-down version of background checks,” Mr. Reid declared in the Capitol, flanked by the families of Newtown, Conn., school shooting victims.
Those families also visited President Obama on Thursday at the White House and Speaker John A. Boehner.
Quiet talks between Senators Mark Begich, Democrat of Alaska, and Kelly Ayotte, Republican of New Hampshire, officially do not exist. Both senators voted no in April, and aides to both deny the existence of negotiations or legislation.
“There are no talks,” said Jeff Grappone, a spokesman for Ms. Ayotte. “There is no legislation. She stands by her vote.”
But other senators are openly acknowledging and encouraging the effort and say the talks are building momentum. Senator Richard Blumenthal, Democrat of Connecticut, said a new version of the gun bill would most likely enhance prosecutions of those who violate existing gun laws and further clarify that new legislation would not and could not lead to a national database of guns or gun ownership.
Other Democrats said the defeated background check measure, written by Senators Joe Manchin III, Democrat of West Virginia, and Patrick J. Toomey, Republican of Pennsylvania, would probably be amended to exempt more rural sales and person-to-person sales from mandatory checks.