The earlier bill, which was opposed by Mayor Michael R. Bloomberg, never came to a vote.
An innovative earlier bill by Ron Wyden, a Democratic senator, has a number of Republican co-sponsors.
Mr. Gregg described the earlier bill as "a lawyers' relief act".
Expect an early bill to 'pave the way' to its abolition.
The Senate majority leader, John L. Sampson, who sponsored the legislation and supported the earlier bill, cited the looming deadline.
But it is a far cry from what they proposed in an earlier bill that was deemed too broad.
Mayoral aides estimated that the earlier bill would have cost the city $100 million when it faces a $5 billion deficit.
Of the three comics on the early bill, only one, Russ Meneve, touched on the topic, and only glancingly.
The council, a powerful oversight agency, had rejected an earlier bill three times, saying it violated Islamic law.
The Assembly speaker, Sheldon Silver, had backed the earlier bill, and it appeared unlikely that the new bill would pass his chamber.
