The Democratic Party’s designated candidate for governor, Attorney General Eliot Spitzer, will be marking the first day of school by sending his running mate, state Senator David Paterson, to a United Federation of Teachers press conference calling on Mayor Bloomberg to shrink class sizes by hiring more teachers.

Mr. Paterson, who is running for lieutenant governor, will be lending his support to a high-profile campaign waged by the teachers union to pressure the city to set aside a chunk of its education budget for increasing the teacher workforce.

Mr. Paterson’s involvement in the union event, where he will be standing beside the president of the UFT, Randi Weingarten, represents a signal by the Spitzer campaign on a key education issue that is emerging as a major flash point between Mr. Bloomberg and the teachers union, a powerful force in Albany.

Mr. Bloomberg and his schools chancellor, Joel Klein, are opposed to mandated class-size reductions and have blocked an effort by the union to amend the city charter by requiring the city to spend more than $1 billion a year on more teachers.

Notably absent from today’s press conference will be Mr. Spitzer himself. Department of education officials said the UFT had indicated to them as late as Friday that Mr. Spitzer would be attending. A union representative said Mr. Spitzer was welcome to come but not formally invited.

“I’ve been saying very clearly we’re going to reduce class size,” Mr. Spitzer told The New York Sun yesterday. “It’s one of the critical ways to improve the educational quality that our kids receive.”

Spitzer campaign officials did not return calls or e-mails requesting comment about the event.

The attorney general, who is friendly with Mr. Klein and has been endorsed by the state teachers union, has treaded carefully over contentious educational issues, offering a broadly conceived platform with elements appealing to both advocates for school choice and union officials on the other side of the spectrum. Both sides say they aren’t sure if Mr. Spitzer will be a partner or an adversary.

“He’s all things to all people,” the Republican nominee for governor, John Faso, who is opposed to the union’s plan for enlarging the teacher workforce, said. He supports attracting more teachers by streamlining the certification process and awarding “incentive pay” to recruits with sought-after skills.

Mr. Spitzer has said he supports lifting the statewide cap on the number of charter schools, which has been championed by Mr. Klein and Governor Pataki but whose growth has been frozen by law at 100. But Mr. Spitzer hasn’t said whether he thinks the schools, which are publicly funded but privately run, should be unionized.

On the issue of class sizes, he has also kept his cards close to the vest. It’s not clear how much money Mr. Spitzer would like to see the city school system spend on hiring more teachers.

“This is an example of General Spitzer clearly saying that he’ll make the decisions that he’ll make when he’s elected governor,” a Democratic political operative and an adviser to Mr. Spitzer’s 1998 campaign for attorney general, Henry Sheinkopf, said. “Why should he tell people now? He gains nothing.”

The conflict over class sizes is heating up as the Campaign for Fiscal Equity lawsuit, a two-decade-old legal dispute over how much money the state owes city schools to ensure that student education meets constitutional standards, appears to be drawing nearer to settlement.

Mr. Spitzer has said if he’s elected, he would push for a negotiated settlement in the case and has said he supports increasing the city school system’s annual operating budget by $4 billion to $6 billion, roughly the amount that the state’s highest court has required the state to pay. He has also pledged not to raise taxes.

Although a settlement is far from guaranteed, both the union and the Bloomberg administration are busy plotting what to do with the additional money.

Ms. Weingarten says she wants 25% of funds from a CFE settlement — or roughly $1 billion to $1.5 billion a year — to be dedicated to hiring more teachers to push down class sizes, which are on average higher in the city than in the rest of the state.

Union officials argue that smaller classes would help even the playing field between poorer and richer students, attract better teachers, encourage more parent involvement, and reduce disciplinary problems.

City education officials have expressed doubts about the benefits of smaller classes, arguing that students would be better off with higher quality teachers. Officials said they would rather spend additional funds stemming from the lawsuit on salary increases and signing bonuses for teachers assigned to less-desirable schools and who teach subject areas, such as math and science, where there is a shortage of educators.

“We don’t believe in mandating class size,” said a spokesman for the education department, David Cantor. “It’s an extremely important tool for improving classroom instruction, but it’s just one tool. Some principals would rather spend the money in developing teacher quality.”

During Mr. Klein’s tenure, class sizes in most grades have dipped slightly. Between fiscal 2003 and 2005, the average kindergarten class has held steady at 20.8 students, while third-grade classes have fallen to 21.5 students from 22.4.

The union has unsuccessfully sought to put a referendum on the November ballot that would mandate that Mr. Bloomberg allocate money toward reducing class sizes. In May, a state Supreme Court justice threw out the referendum, concluding that it would improperly interfere with state control of educational matters. Tomorrow, an appellate court is scheduled to hear oral arguments on the appeal. With its effort stalled in court, the next step for the union could be lobbying the state Legislature and the next governor to establish new laws on class sizes.

Conservative and centrist think tanks have questioned the link between class size and educational achievement. “While smaller class sizes are popular with parents, teachers, and politicians, they can have an unintended detrimental effect on teacher quality,” a 2005 report from the Progressive Policy Institute said. Eric Hanushek, now a fellow at the Hoover Institution, has written, “A thorough review of the scientific evidence provides no support for broad programs of class size reduction.”