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Lawmakers in Albany, seeking to send a message to the nation that the recent mass shootings demand swift action, say they hope to vote on the package of legislation as soon as next week.

The Assembly speaker, Sheldon Silver, a Manhattan Democrat, told reporters on Wednesday that Mr. Cuomo and legislative leaders were "95 percent" of the way toward an agreement. Senate Republicans, considered the only possible obstacle to the governor's proposal, indicated they did not intend to block a deal.

"When you hear about these issues all across the nation, whether it's in the movie theater in Aurora, Colo., or Columbine, something needs to happen — something transformative," said Senator Timothy M. Kennedy, a Democrat from Buffalo.

The dash to enact new gun controls made New York the first flash point in the battles over firearm restrictions that are expected to consume several state capitals this year.

But the debate also raged elsewhere on Wednesday, from Denver, where supporters of gun rights rallied to oppose weapon restrictions in the new legislative session, to Connecticut, whose governor, Dannel P. Malloy, in an emotional speech to lawmakers — he lost his composure talking about the mass killings at a Newtown elementary school last month — said, "More guns are not the answer."

At the White House, Vice President Joseph R. Biden Jr. met with gun-control advocates and said the Obama administration planned both to pass legislation and to use executive orders to try to reduce gun violence. "The president and I are determined to take action," Mr. Biden said. "This is not an exercise in photo opportunities."

Mr. Cuomo's aides said the proposed legislation in New York would expand the definition of what is considered an assault weapon to match California's law, currently the most restrictive in the nation. But the overall package would go further, they said, by limiting detachable ammunition magazines to 7 rounds from the current 10, and requiring background checks for purchases of ammunition, not just weapons.

Limiting magazines to seven rounds would give New York the toughest restrictions in the nation. Only around half a dozen states currently limit the size of magazines, and most of them allow magazines that contain up to 10 rounds, according to a survey by the Law Center to Prevent Gun Violence, which advocates gun control. The New York law would also close a loophole that has thwarted enforcement of limits on the size of magazines.

Even as Mr. Cuomo detailed his plans, gun-rights groups mobilized to oppose the new restrictions.

"We fully expect that New York state's gun owners will be completely engaged in this debate and N.R.A. will be there to lead them," said Chris W. Cox, the chief lobbyist for the National Rifle Association, which has donated more money to state politicians in New York than anywhere else, much of it to Senate Republicans.

And immediately afterward, Budd Schroeder, the chairman of the Shooters Committee on Political Education, a New York gun-rights group, said he planned to meet with every state senator he knew to ask them to stand up to the governor.

"The legislators are going to be getting a lot of phone calls in their district offices," Mr. Schroeder said. "How is taking away my rights to own any type of firearm I choose going to change the attitude of a criminal?"

Yet Mr. Schroeder's group, on its Web site, acknowledged the challenging terrain. "We can say with certainty," it warned, "that anything short of overwhelming our legislators with calls, e-mails and letters, we have virtually no chance."

Mr. Cuomo's initiative drew praise from Mayor Michael R. Bloomberg, who has made gun control his signature cause. "I was particularly struck by his passionate leadership on gun violence," Mr. Bloomberg said in a statement. "New York State has led the nation with strong, common-sense gun laws, and the governor's new proposals will build on that tradition."

Mr. Cuomo is a possible 2016 presidential contender who is seeking to elevate his stature among Democrats base nationally, after a much-praised victory on same-sex marriage in his first year in office. His push for enhanced gun control even drew praise from Cardinal Timothy M. Dolan of New York, in a letter that otherwise criticized Mr. Cuomo's support for abortion rights.

Mr. Cuomo had already stirred up anxiety among gun rights groups by saying in a radio interview in December that "confiscation could be an option" for existing assault weapons.