While both Mayor Bloomberg and the City Council speaker, Gifford Miller, have said they will wait until after the presidential election to gear up their mayoral campaigns, they took the opportunity last week to bare their campaign fangs – and sink them into Council Member Eva Moskowitz.

Until last week, Ms. Moskowitz had been permitted to do pretty much as she liked on education. As head of the council’s Committee on Education, she held hearings on the teachers contract and targeted the onerous “work rules” it retained, including using longevity as the sole criterion for teacher assignments and maintaining obstacles to the firing of incompetent teachers.

While Mr. Miller made clear behind the scenes he wasn’t happy about the high-visibility hearings called by Ms. Moskowitz, his longtime ally in East Side Democratic politics, he held his fire. Mr. Bloomberg muttered that the hearings were not particularly helpful at a time when negotiations were going on.

That all changed Tuesday, when Ms. Moskowitz hand-delivered a letter to the mayor urging him to make good on his promise to reform the work rules in the teachers contract. She said she was concerned that he’d back down, in his haste to make peace with the United Federation of Teachers. Then she made the letter public.

The response was rapid. Within hours Mr. Bloomberg denounced Ms. Moskowitz for “grandstanding” and Mr. Miller called her letter “destructive to the process.”

The stinging rebuke should be seen as one of the opening volleys in next year’s mayoral campaign, a political consultant, Hank Sheinkopf, said.

“Eva found out last week what it is like to play in the big leagues,” he said. “These guys are in campaign mode now. She has said that she would like to run for mayor in the future, so they just let her have it. The mayor and the speaker are jockeying for position on education, and Eva got in the way.”

Other observers agree. For Mr. Bloomberg, forging a teachers contract is key. The teachers have been working without one for 17 months and the mayor is eager to resolve the issue, not only so he can prove he is managing the city well, but also so he can prevent the teachers from mounting a serious grassroots effort against him in advance of next November’s election.

Mr. Miller, for his part, believes he will be the Democrat left to challenge Mr. Bloomberg after the primary. He wants the union’s endorsement.

Both men came to the conclusion they could win some political territory by lashing out at Ms. Moskowitz, analysts said.

“I was a little surprised that they went into attack-dog mode,” Ms. Moskowitz told The New York Sun, adding that she thought her letter to the mayor was “rather complimentary” and had highlighted all the good things he had already done to start reforming the city’s public schools.

“In terms of Gifford, reasonable people can differ,” she said. “He has taken the more conventional view that you don’t speak out on this issue of the contract this late in the negotiations. In my view, the conventional wisdom hasn’t gotten us very far in terms of children’s education.”

While no one is willing to discuss the details of the contract negotiations on the record, a broad outline of the discussions has emerged from people on both sides of the talks. The deal could include pay raises of up to 14% over three years, in return for teachers working an extra week at the start of the school year and perhaps working a longer school day during the year.

Also discussed has been the use of pilot programs to start to whittle away at the bastions of preserving longevity and resisting merit pay.

Another change that the negotiators have talked about is the introduction of some sort of sliding scale of pay for much-needed math and science teachers.

What is unclear is whether those discussions are continuing and will be reflected in a final contract or whether the city administration has said pilot programs are not enough to satisfy Mr. Bloomberg that the work rules have fundamentally changed.

All this talk of the teachers contract flared because of a Yankees game.

Randi Weingarten, president of the teachers union, showed up in Mr. Bloomberg’s box with the mayor during a playoff game last month, and the speculation has been rife ever since. Mr. Bloomberg said nothing should be read into her appearance. But those close to Ms. Weingarten said she was well aware that being at the game with the mayor would send a message. “She has a political constituency, too,” one observer close to the union leader said.

Ms. Moskowitz, for her part, said she would not allow last week’s attacks to deter her from keeping the mayor’s feet to the fire.

“There is the politics of education reform on one level, but the other level is that this contract not only doesn’t put children first, but it doesn’t put teachers first,” she said. “If you are a teacher in a school where you don’t have supplies and your kids are coming from poor circumstances, it is already challenging enough. If on top of that you are inheriting kids whose last teacher shouldn’t be a teacher and you are having to make up first and second grade in your classroom, that’s an issue we ought to be talking about.”

Representatives of the teachers and the Bloomberg administration are scheduled to return to the bargaining table this week.