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In addition to more comprehensive background checks, Mr. Obama is calling for tougher laws against gun trafficking and straw purchases.

Mr. Obama and Vice President Joseph R. Biden also have lobbied hard for a ban on semi-automatic firearms modeled after military assault weapons. But Mr. Reid dropped the assault-weapons ban from the broader bill two weeks ago, saying there were not enough votes to pass it in the Senate.

The ban, proposed by Sen. Dianne Feinstein, California Democrat, still can be offered as amendment, but it won’t be part of the base bill Mr. Reid is fashioning that faces an all-but-certain Republican filibuster.

After Mr. Obama’s renewed push Thursday, Mr. Reid’s spokesman angrily denounced the threat by a handful of Republicans to filibuster the broader gun legislation.

“While this threat is entirely unsurprising, it’s outrageous that these senators are unwilling to even engage in a debate over gun violence in America,” said Reid spokesman Adam Jentleson. “No matter your opinion on this issue, we should all be able to agree with President Obama when he said that the children and teachers of Newtown, along with all other Americans who have been victims of gun violence, at least deserve a vote.”

Ranking member Chuck Grassley of Iowa, who voted against the measure in committee, is reportedly crafting his own gun bill as well — a move that could undercut attempts to lure more Republicans and red-state Democrats to sign onto the package Mr. Reid intends to bring to the floor next month. That package also includes bills that did receive a modicum of bipartisan support: a bill intended to crack down on gun trafficking and straw purchasers (though Mr. Grassley was the only Republican to break ranks on that measure) and another intended to bolster school safety efforts.

The National Rifle Association and Republicans in Congress have fiercely opposed the assault-weapons ban, and the package faces an even more difficult road in the GOP-controlled House.

The White House event Thursday morning was coordinated with other rallies and gatherings planned in cities across the country on what supporters called “a national day of action.” The killer in Newtown used a semi-automatic rifle that would have been banned under Mrs. Feinstein’s proposal.