ALBANY – Negotiators at the Capitol have spent the past three days trying to iron out a deal to add new controls to assault-style weapons and other gun restrictions in the wake of the Sandy Hook Elementary School shootings.

But the sides are still apart, and a push by Gov. Andrew M. Cuomo to bring lawmakers back to Albany before Christmas is dead, though the governor and legislative leaders are still not completely ruling out a special session to take up the issue before the end of the year.

Cuomo, who has his eyes on a possible White House run in 2016, had been pushing hard, sources said, to get lawmakers back to town by today to try to become the first state to enact stronger gun laws since the killings last week in Connecticut.

But Thursday on an Albany radio station, Cuomo said there was still “a big difference of opinion’’ between the sides.

“I highly doubt it,’’ he said of the possibility of a special session before the end of the year.

Assembly and Senate members were told Thursday there would be no special session this week, but legislative leaders also told them to be prepared for a possible return by Jan. 1.

According to officials speaking on condition of anonymity, the talks involve new limits on sales of assault-style weapons, on large-capacity ammunition magazines, and more severe penalties for crimes involving guns. Assembly Democrats have been pushing to require periodic re-registration of gun licenses – one plan calls for once every five years. Some downstate localities, including New York City, have such re-registration requirements. “We’re having meaningful conversations,’’ Mike Whyland, a spokesman for Assembly Speaker Sheldon Silver, said Thursday.

Gun rights advocates questioned Cuomo’s motivations for the push. “I think he’s trying to set the stage for a run for president in four years and right now this idea of stricter control is in the hot spot because of the real disaster that happened in that school,” said Budd Schroeder, chairman of the Shooters Committee on Political Education, a Buffalo-area gun owners rights group. “So he’s going to take advantage of the moment and generate as much publicity as possible. I think it’s just pandering.” Schroeder said some of the ideas being discussed in Albany would make many commonly purchased guns illegal.

“New York has one of the stricter gun control laws in the nation, and it doesn’t work any better than the no-gun-control laws in Vermont … They’re trying to use this event to deny people in New York State the constitutional right to keep and bear arms,’’ he said.

If there is no deal, Cuomo will outline his ideas on the topic in his Jan. 9 State of the State address. The rushed timing led to much speculation that officials also were trying to push through other issues before the start of a new legislative session – one that will feature an untested power-sharing deal in the Senate between Republicans and five breakaway Democrats.

Before Hurricane Sandy hit, all sides thought a special session was certain to take up issues like a minimum wage hike and a legislative pay raise. But officials said even if there is a special session, lawmakers recognize they could be committing political suicide by giving themselves a pay raise under the cover of returning to Albany to enact gun legislation.

The new leader of the main Democratic conference in the Senate endorsed the idea of quickly dealing with gun legislation. “As elected leaders, we have an obligation to move beyond partisan ideology and political platforms,” said Senate Democratic Conference Leader Andrea Stewart-Cousins. “The Senate Democratic Conference has been a longtime supporter of common-sense gun laws, and we welcome news that a special session to address these laws is being discussed. We stand ready to offer our support.”

Scott Reif, a spokesman for the Senate Republicans who have full control over the Senate until Jan. 1, said “There are no plans for a special session.”

In Albany, saying there are “no plans” usually means, in the end, no one is really certain if this deal can be pulled off, or when. Negotiators for the Senate, Assembly and governor’s office were to return to the negotiating table this morning.

Further, a source close to the coalition group that will control the Senate in January – Republicans and five breakaway Democrats – told The Buffalo News on Thursday that Senate Majority Leader Dean Skelos and Independent Democratic Conference Leader Jeff Klein have been speaking regularly about a variety of issues over the past two weeks. “Right now, gun control is chief among them,” the official said, speaking on condition of anonymity.

The official said the two senators “are committed to finding common ground on the issue.”

In his radio interview, Cuomo, a shotgun owner, said he understands there is a “balance” that needs to be considered in the gun debate. “I understand the rights of gun owners … The question is, on the other side, is the availability of assault weapon-type guns to people who, as we’ve seen, have the potential to do tremendous damage,” he said.

Officials close to the talks said Senate Republicans – sensitive to its members, especially in conservative upstate districts – have balked at a number of the gun control measures on the negotiating table. Cuomo himself noted that many GOP senators take campaign money from the National Rifle Association. But, he added, “I wouldn’t say that the Republican Senate is against reforms on guns.”