ALBANY, N.Y. — Governor Andrew M. Cuomo, pushing New York to become the first state to enact major new gun laws in the wake of the massacre in Newtown, Conn., plans on Wednesday to propose one of the country’s most restrictive bans on assault weapons.

New York is one of seven states that already ban at least some assault weapons. But Cuomo has described the existing law as having ‘‘more holes than Swiss cheese,’’ and he wants to broaden the number of guns and magazines covered by the law while also making it harder for gunmakers to tweak their products to get around the ban.