Los Angeles school district officials and employee unions announced an agreement Saturday to cut five days from this school year and seven days next year in an effort to maintain up to 2,100 campus jobs.

If approved by members of the teachers and administrators unions, the move would save the Los Angeles Unified School District about $140 million and preserve class sizes in grade and middle schools, officials said. The district, the second largest in the nation, is facing a $640-million deficit.

District officials had been urging unions for months to make concessions to help balance the books. Administrators agreed to the furlough days Monday night, and the teachers union reached a deal late Friday, representatives said at a news conference.

“It is extremely important in going forward that we have this kind of partnership,” said Supt. Ramon C. Cortines, who had occasionally appeared frustrated that the groups had not joined others in taking action to help the district with its budget crisis.

Under the plan, educators would have two extra paid, student-free professional development days next year.

Officials said they expect members of the unions to approve the shortened school years, particularly since they will save jobs and the pay cut is temporary.

The district, along with others throughout the state, is reeling from one budget shortfall to another. Districts have laid off teachers and increased class sizes, and some are considering closing schools. L.A. Unified has avoided that option; like others, reducing the calendar came as a last resort.

For working parents, the shortened calendar could mean child-care problems and other issues.

Under a new state law aimed at easing school districts’ budget deficits, districts still will receive full funding for a year even if they eliminate some instructional days.

All L.A. Unified schools would be closed the Friday before Memorial Day weekend, and each campus would also cut four days at the end of this school year.

Teachers, a union representative said, will have to cram instruction into a shorter calendar. “We are concerned for the quality of education for our students,” said Julie Washington, a vice president with United Teachers Los Angeles.

Cortines proposed in February cutting six days from this school year, even though he had previously opposed a reduction because he feared it would hurt instruction.

“Our people will be asked to do more with less,” he said at a Saturday morning news conference at the teachers union headquarters.

The agreement will allow about 1,800 teachers, 100 administrators and 300 librarians, nurses and counselors to keep their jobs. The district agreed that it would not seek further pay reductions for administrators.

The school board voted this month to send preliminary layoff notices to about 5,100 employees. But A. J. Duffy, president of the teachers union, said he believes that many of his members could be brought back to the classroom through other methods and hopes that only several hundred would be in danger of losing their jobs.

Duffy said he believed his membership would approve the deal even though it amounts to a temporary pay cut. Union officials have said that furlough days are a better alternative to a permanent pay reduction.

“If it’s a fair deal, we’re willing to take furlough days,” Duffy said.

Several unions, including those representing cafeteria workers and bus drivers, have agreed to take unpaid days. Many non-unionized district employees, including upper management, have also begun to take furlough days. Staff members for the Board of Education have agreed to take four unpaid days.

Duffy said he would continue to press the district to make reductions to L.A. Unified’s bureaucracy, something Cortines agreed was necessary.

“He must have got my memo,” Duffy quipped.

As part of the budget discussions, Cortines, teachers and administrators agreed that groups seeking to take control of low-performing schools next year will have more time to apply. Teachers and administrators had complained that they were not given enough time to develop plans and solicit support this year, the first under a new district policy that allowed groups to take over some campuses.

jason.song@latimes.com