They offered to spend up to $50 million for asbestos cleanup in schools under a formula that favors suburban districts.
The agency said the testing, along with the asbestos cleanup and testing program announced in May, will be the largest cleanup in its history.
"Where they're doing asbestos cleanup."
The suit sought the asbestos cleanup so that the school, in Crown Heights, could be reopened as soon as possible.
The Governor and Mr. Miller offered to spend up to $50 million this year for asbestos cleanup under a formula that favors suburban schools.
The higher figures will mean that other school construction and renovation projects will have to be delayed to pay for the asbestos cleanup, disappointing parents and politicians across the city.
One of every eight dollars spent on school construction this year will go to the asbestos cleanup.
Administration officials have said that asbestos cleanup is a local responsibility and that the most serious cases have already been eliminated.
The asbestos cleanup is still unfinished in the main building.
A 2001 explosion at the Lovett Generating Station, in Stony Point, injured a worker and required an asbestos cleanup.