Facing pressure to grant the city authority to stop paying teachers in the so-called Absent Teacher Reserve, teachers whom school officials say “either can’t or won’t get a job” but are still on the city’s payroll, the United Federation of Teachers is fighting back.

In a data analysis released to The New York Sun yesterday, the union challenged the notion that teachers in the reserve pool do not hold actual jobs. Nearly one-third of teachers in the pool, or 194 of an estimated 665, are not idly waiting for work but are rather teaching full courseloads, according to the analysis, which union officials said was compiled from a combination of central labor records available to the union and anecdotal reports from schools.

The analysis also disputes an estimate, published in a report last week and endorsed by city school officials, that the reserve pool has cost the city $81 million over the last two years.

According to the union’s analysis, when factoring for the money reserve pool members save in covering full courseloads and substitute teaching, their cost is $18.7 million annually.

The union president, Randi Weingarten, is also reaching out to members of the reserve pool with a promise to reject any change in the contract that would dent a “rock-solid job security clause” for ATR members.

“I wanted to personally reassure you that the UFT will not reopen the contract to negotiate any change in the terms and conditions of your employment,” Ms. Weingarten wrote in a letter to reserve pool members on Friday.

The hard line makes it extremely unlikely that the Bloomberg administration will be able to negotiate the deal it would like to cut on the Absent Teacher Reserve question.

For seven months, the administration has been holding private meetings with the union seeking some way to either fire or cut the pay of members of the pool. Such a change would be historic in city schools long ruled by union efforts to create air-tight job security. The meetings all ended in stalemate.

Hopes that Ms. Weingarten might relent seemed to rise with last week’s report by the New Teacher Project, a nonprofit group that does some contracting work with the city.

The report found that reserve teachers who remained in the pool without finding a job were more likely to have been rated “unsatisfactory” and less likely to have actively sought a job. To cut the cost of the pool, it suggested the city create incentives for members to leave it, such as a threatened pay cut if they stayed for 12 months.

The union analysis disputes the report’s characterization of reserve teachers. It charges that ATR status, rather than suggesting poor quality or a lack of motivation, has actually become an accounting trick. Because ATR members’ pay and benefits are covered by central administration, not individual school budgets, using them as full-time teachers is a way for principals to add staff without losing money, the union says.

One ATR member, John Murray, a 29-year veteran of the school system, said he was substituting last semester but now teaches art history at Stuyvesant High School full-time, drawing on a recent sabbatical he used to study the subject at the American University of Rome.

The UFT’s list of schools using ATR members to teach full-time loads includes several with multiple teachers who are ATR members, such as Tilden High School in Brooklyn, where the union says 14 full-time teachers are actually members of the ATR.

Told about the union’s analysis yesterday, Department of Education officials dismissed it.

“I believe this is a red herring of the first order,” Deputy Chancellor Christopher Cerf said. “I believe there is no possibility that her number is accurate.”

The president of the New Teacher Project, Timothy Daly, said he knew of no way to collect data on precisely what ATR members are doing inside schools.

“Why didn’t I hear about this before now if this is a widespread problem?” Mr. Daly said.

Mr. Cerf said the city still faces a troubling question: how to handle the significant number of teachers who are guaranteed essentially lifetime employment by the teachers contract but “either won’t get a job or can’t get a job.”