Days after Mayor Bloomberg vowed to slash the number of parking permits handed out to city employees, the powerful teachers union is thrashing.

Mr. Bloomberg’s plan calls for a 20% reduction in the permits, which grant employees ranging from police officers to court clerks to teachers access to select parking spots. He billed it as a way simultaneously to cut down on abuse of the permits — a coveted perk for many government workers — and to unclog the city’s streets and air, by encouraging workers to switch into subways and buses and out of carbon-emitting cars.

On Friday, the president of the United Federation of Teachers, Randi Weingarten, objected to Mr. Bloomberg’s inclusion of teachers in the cutbacks, sending him a scathing letter calling the idea “deeply disturbing.”

She said teachers should not be lumped in among those abusing the permits. In fact, union officials said, teachers — some of whom work in places where no subway lines go — have far too few permits, forcing many to go to extraordinary measures to find a place to put their cars.

Teachers often make informal deals with local residents to rent out driveway space, a UFT vice president, Michael Mulgrew, said. One school where he used to teach, in Brighton Beach, had just three parking spots for a staff of 130, he said.

Schools in the past have also paved over playgrounds to make space for parking lots.

In her letter, Ms. Weingarten said cutting back teacher permits would damage the city’s efforts to attract highly qualified teachers to poorly performing schools.

“Holding abusers of parking privileges accountable for their actions should not be done at the expense of teachers whose jobs are hard enough already,” she wrote.

Announcing the plan, Mr. Bloomberg said his intention was not to prevent city workers from doing their jobs but to curb abuse of the permits, which reports have shown are sometimes used to double-park or park in illegal places, such as on crosswalks and in front of fire hydrants. “We will give out placards only to those who need to use them to further the public interest,” he said.

All city agencies, including the Department of Education, have been asked to begin plans to reduce the number of permits they will give out by 20%.

Because each agency hands out the permits on its own, there is no precise figure on the total number circulating. City Hall put its guess at 75,000, while an advocacy group, Transportation Alternatives, has said the number is much higher, more than 150,000.

The precise number of teachers who have permits is also not clear.

A spokesman for the Department of Education, David Cantor, said the agency gives out “tens of thousands” of permits each year.

Some go to teachers and principals, who can use them to park outside their schools during school hours, while others go to other officials, such as superintendents and central office aides, who get wider parking access.

In a recent report, Transportation Alternatives estimated that teachers held 50% of all the city’s permits, or 75,000.

The group’s communications director, Wiley Norvell, said teachers should not be exempt from regulations.

“Wherever these permits are in use, they’re abused on some level,” he said.

Transportation Alliance has published photographs on a watchdog Web site, uncivilservants.org, cataloguing illegally parked cars with Department of Education permits.

Mr. Norvell said teachers also have an extra obligation to decrease their car traffic: It would make children safer from crashes and from carbon emissions, which are linked to exacerbated asthma.

Mr. Mulgrew laughed at the 75,000 figure for schoolteachers, which is nearly the same as the total number of educators now teaching in city schools. He said the UFT has been asking the Department of Education to send more permits to teachers for at least 10 years — and has seen no increases.

A City Hall official said it is possible the policy reconsideration Ms. Weingarten requested will happen. A working group spearheading the reduction will consider agencies’ requests for more permits, if they make them, the official said.