Mayor Bloomberg said yesterday he would not let the police and fire unions bully him into giving them a larger pay increase by threatening to strike during the Republican National Convention.

“The city won’t be embarrassed” by a strike during the convention, Mr. Bloomberg told reporters. “Anyone who thinks there is pressure on the administration because the convention is coming doesn’t seem to understand what New York is all about.”

Police and fire union officials have said they won’t rule out a strike or a sickout during the convention even though such a work stoppage would be illegal.

Union officials leaders cannot call a strike, but if members decided to stop work, the leaders could throw up their hands and say they can’t control their rank and file.

“We’re still in arbitration,” said a Patrolmen’s Benevolence Association spokesman, Joseph Mancini. “They asked for 3% in productivity gains and are willing to give back 1% in a salary increase in exchange. That’s a losing proposition.”

Mr. Bloomberg said the city’s uniformed services understood their obligation not to strike or try to use the convention, set to start August 30, as leverage against the city.

Off-duty police and firefighters have been taking advantage of the mayor’s embrace of free speech by dogging his heels at virtually every turn. “Forget the praise, give us a raise,” a dozen policemen chanted as the mayor arrived in Brooklyn to swing a couple of golf clubs.

Mr. Bloomberg, in shirtsleeves, grimaced as he got out of his car.

On the way out, the group was no less vocal. “Give us our pay,” they sang out, “we’ll go away.”

Mr. Mancini said the PBA is willing to negotiate with the city, but the mayor isn’t offering anything the members can accept. The city has offered the police and firefighters the same deal they forged with District Council 37 and several other smaller unions: a 15% raise plus $1,000 over three years. Some 2% of that increase is supposed to come from productivity enhancements such as longer hours or a change in vacation days or benefits for new hires.

Mr. Bloomberg reiterated that offer yesterday and tried to bring down the volume on the growing war of words. His press secretary, Edward Skyler, called the union members harassing the mayor “thugs” on Tuesday. Mr. Bloomberg said he wouldn’t get into name-calling.

“I wasn’t brought up that way,” he said, declining to repeat Mr. Skyler’s epithet. At the same time, he did stay firm against the unions. “Rest assured. I will not be intimidated by anything. This mayor is a little tougher than that.”