Gov. Robert F. McDonnell unveiled a program Tuesday that would award $3 million in merit-based bonuses to recruit and retain teachers in select schools in Northern Virginia and elsewhere in the state.

But the experiment in merit pay prompted concern in some school districts. Officials in Fairfax and Loudoun counties said they probably would reject the money even though McDonnell (R) was offering it at a time of strained budgets.

The resistance highlights how controversial merit pay remains in public education, despite the support of the Obama administration and some other school reform advocates. Schools in Prince George’s County and the District have programs that tie teacher pay, at least in some instances, to evaluations of performance. But teachers unions often oppose such plans.

McDonnell named 169 eligible schools, including about 50 in Northern Virginia, that he said have been difficult to keep staffed. Nine of those schools are in Fairfax County, but the district’s experiment with merit pay in the 1980s did not go well, said Superintendent Jack D. Dale.

“We are not planning to apply for any pay-for-performance grants,” Dale said. “We previously had a performance-pay system in Fairfax that was ultimately not successful.”

School districts have until June 15 to apply for McDonnell’s program, which is to begin in the fall. “The funding available for performance pay represents an opportunity to provide meaningful incentives and rewards for exemplary teachers in a significant number of Virginia schools,” McDonnell said in a statement to reporters.

Whether such programs succeed hinges largely on the criteria used to evaluate teachers. McDonnell plans to require that districts accepting the merit-pay funding also adopt a newly overhauled teacher evaluation system, driven largely by student performance on the state’s standards of learning tests, often called SOLs.

Similar approaches have drawn the ire of teachers unions, which view test scores as poor measures of teacher performance, even when such metrics focus on student improvement from one year to the next, as Virginia’s will.

“Paying teachers to work in hard-to-staff schools is one thing, but it’s totally different to allocate pay based on how students do on an SOL on a given day in a given year,” said Kitty Boitnott, president of the Virginia Education Association.

Attempting to tackle the issue exclusively in schools that McDonnell dubbed hard to staff would seem to make the initiative more palatable. But Northern Virginia officials said they were puzzled by the governor’s list.

“They’ve listed five of our schools, and none of them are difficult to staff,” said Wayde Byard, a spokesman for the Loudoun County school system. The district is unlikely to participate in the program, he said, but the prospect will be discussed next week at a meeting.

“We’re not really sure how these schools got on the list rather than others,” said Linda Erdos, a spokeswoman for the Arlington County school system. Some of the schools on McDonnell’s list are among the district’s more successful, she said, while some of its more troubled schools were left off.

Fairfax’s attempt at merit pay in the early 1980s illustrates the costs of such a failure, some teachers said. “The program was underfunded . . . and it caused employees to be rated lower than they should have been. It really damaged relationships at schools,” said Steve Greenburg, president of the Fairfax County Federation of Teachers.

State officials say they have learned from that experience and others in the past two decades. Evaluation systems have been honed, they say, and the funding this time is sufficient.

Prince William County will launch an $11.1 million merit pay program next year in its 30 poorest schools, but that initiative will allocate awards based on the overall performance of schools, not individual teachers.