Pedicab drivers are gearing up to fight for their right of way as the city seeks to impose restrictions on the decade-old tourist trade.

With the City Council and administration officials negotiating the idea of regulating the pedicab industry for the first time, a hearing on two competing bills is set for today. The proposals would set a $125 annual licensing fee for a first cab, and $70 for each additional vehicle. The regulations would also require seatbelts, mandate that pedicab owners have insurance, and limit the number of passengers to two adults and a small child.

The pedicab trade group supports permit requirements for owners of the bicycle-led carriages, but it says some of the proposed restrictions, including a citywide cap and a ban on riding in parks, go too far. “We believe the fix is in,” the president of the New York City Pedicabs Association, George Bliss, said. Mr. Bliss has hired a lobbyist to try to prevent the measure from becoming a “Frankensteinian monster,” he said.

Pedicabs have become increasingly popular, especially among tourists, since they first hit the city streets in the mid-1990s, and there are now about 300 operating in New York. While the city’s tourism office, NYC & Company, has voiced support for the vehicles, the taxicab industry has railed against pedicabs, saying they clog the streets, create safety hazards, and take away business.

Council Member Alan Gerson, who represents Lower Manhattan, said he supports softer restrictions than the administration is now proposing. Instead of capping the number of pedicabs citywide, Mr. Gerson said he would restrict their use in certain locations during rush hour. He also supports allowing pedicabs to be powered by electric motors, which the administration wants to ban.

“I’m very confident that we’ll come up with a reconciled bill that protects New Yorkers, visitors, and the viability of the industry,” he said. Officials are looking to finalize the bill in the next several weeks, Mr. Gerson said.