“We don’t need another tragedy to point out the problems in the system,” Mr. Cuomo said at a news conference.

“Enough people have lost their lives,” he added. “Let’s act.”

The expanded ban on assault weapons would broaden the definition of such weapons, banning semiautomatic pistols and rifles with detachable magazines and one military-style feature, as well as semiautomatic shotguns with one military-style feature. New Yorkers who already own such guns could keep them but would be required to register them with the state.

“The message out there is so clear after Newtown,” said the Assembly speaker, Sheldon Silver, a Democrat from Manhattan. “To basically eradicate assault weapons from our streets in New York as quickly as possible is something the people of this state want.”

In an acknowledgment that many people have suggested that part of the solution to gun violence is a better government response to mental illness, the legislation includes not only new restrictions on gun ownership, but also efforts to limit access to guns by the mentally ill.

The most significant new proposal would require mental health professionals to report to local mental health officials when they believe that patients are likely to harm themselves or others. Law enforcement would then be authorized to confiscate any firearm owned by a dangerous patient; therapists would not be sanctioned for a failure to report such patients if they acted “in good faith.”