A day after the police commissioner appeared to side with the police union against Mayor Bloomberg, the mayor lashed out at the union, threatening to challenge a law that allows the union to arbitrate its contract with the state, not the city.

The mayor’s comments signaled that he is digging in his heels in the contentious negotiations with the union, even after Commissioner Raymond Kelly suggested this week that members of the union, the Patrolman’s Benevolent Association, should be given raises above those of the rest of the city’s unions.

“We’re not going to go back to a life of crime in this city, but we are also not going to pay any one union more, outside the pattern. Period, end of story,” Mr. Bloomberg said, referring to a system of negotiating similar contracts for all of the city’s unions known as pattern bargaining.

The city is currently facing a potential shortage in police recruits, a situation some have blamed on low starting salaries negotiated during the last contract.

Yesterday, the mayor praised the state’s Public Employment Relations Board after it agreed to appoint an arbitration panel that will make a final decision in the contract negotiations.

Hours earlier, however, he warned that he might seek to reverse a law allowing the state agency to arbitrate contracts with the police union if final decision breaks the pattern — a possibility if a state panel decides in the union’s favor.

Before 1998, the city’s Office of Collective Bargaining — controlled by the mayor — acted as the mediator in contract negotiations, a system the police union fought to change because it said the agency wasn’t independent. To reverse the law, the mayor would have to have legislation introduced in the state Legislature.

A spokesman for the PBA, Albert O’Leary, said the union would not comment on the mayor’s remarks.