New York City could lose $1 billion in education aid from the state, forcing the nation's largest school system to cut more than 21,000 teachers, Mayor Michael Bloomberg said Friday.

As Gov. Andrew Cuomo prepares to unveil his first budget proposal since taking office on New Year's Day, Mr. Bloomberg and his new schools chancellor, Cathie Black, are bracing for what could be devastating cuts to city schools.

On his weekly radio show Friday, Mr. Bloomberg stressed that he has yet to receive word of a definitive budget proposal from the governor. "Scuttlebutt is that the education budget will be cut statewide, and New York City's share of that would be a billion-dollar cut," he said.

If the governor proposes a $1 billion cut and the Legislature approves it, the mayor estimated the city would be forced to cut 15,000 teachers, most of which would be accomplished through layoffs. That's on top of plans, outlined by the mayor in November, to cut 6,166 teachers in the fiscal year beginning July 1.

In total, the administration is facing the specter of losing 21,000 teachers in the coming months, most through layoffs. An aide to the mayor warned that these numbers would probably change as negotiations with lawmakers over the state and city budgets begin in earnest in the coming weeks.

The city's Department of Education currently employs roughly 75,000 teachers.

Josh Vlasto, a spokesman for Mr. Cuomo, said it's "premature to speculate about the budget" that the governor will release Tuesday. He declined to comment further.

A seniority rule in state law requires that the teachers hired most recently be the first to face layoffs. As a result, city officials estimate that every teacher hired during the past five years would be let go if the state moves forward with a $1 billion cut in aid to city schools.

Mr. Bloomberg said this tenure rule means the city will "have to part company with some of the best teachers." And because new teachers are typically employed in communities that are struggling the most, these layoffs would "disproportionately hurt the schools with more minorities," he said.

The mayor and his new chancellor have launched an intense lobbying campaign to persuade the state to change the law regarding last in, first out.

On Friday, Ms. Black said she would "fight tooth and nail to keep the best teachers in the classrooms. It cannot be about whether a teacher has been in the system for two years or 22 years."

If the seniority law remains in place, parts of the South Bronx could lose 27% of their teachers due to the prevalence of rookie teachers in the area, she said. Other more affluent neighborhoods would lose half that.

"The budget situation is very dire, and any major cutbacks are going to translate into real job losses," said Ms. Black, adding that she and the mayor will fight as hard as they can to avert as many teacher layoffs as possible.

But Michael Mulgrew, president of the United Federation of Teachers, criticized the mayor and Ms. Black for focusing attention on the seniority issue.

"It seems the mayor and chancellor know a lot about how they want to fight for how to do layoffs—and not fight for the children of New York City to not do layoffs," Mr. Mulgrew said.

"No matter what happens, if we do layoffs, kids are going to get hurt," said Mr. Mulgrew, who argued that the state should maintain a tax on people earning more than $200,000 that is set to expire at year-end.

Mr. Mulgrew said the seniority laws are in place to guard against layoff decisions based on age, race, gender or cronyism. "Perhaps the mayor likes cronyism," he said, a pointed reference to his controversial selection of Ms. Black, a former media executive with no prior experience in education.

City Council Member Robert Jackson, chairman of the council's Education Committee, described the possibility of reducing the number of teachers by 21,000 as "absolutely insane, crazy." These types of cuts would be "devastating" and "just outrageous," he said.

"The governor has to look at whether or not the whole system is going to collapse," said Mr. Jackson, pledging to fight to restore the budget cuts. "Class size will be up to 35, 40 kids in a class, if you have to cut 21,000 teaching positions. I can't imagine it, quite frankly."

On Friday, the mayor said he's sympathetic to the governor, who is scrambling to combat a deficit of roughly $10 billion.

"Andrew Cuomo was brought in to balance the budget. He didn't create the situation. But he's got to deal with it," he said. "And it's Medicaid and education—two things everybody says don't cut. But those are the things where all the money is."

"But it's going to hurt," Mr. Bloomberg added. "Unless we can find something else, it's going to cost us an awful lot of jobs."

Mr. Bloomberg is scheduled to present his preliminary budget for the upcoming fiscal year by mid-February. The mayor is looking to fill a gap of $2.4 billion. But as his budget director, Mark Page, testified last month, that gap could swell to $4.4 billion depending on how much aid Albany cuts to the city.

Write to Michael Howard Saul at michael.saul@wsj.com