The Rotunda on the campus of the University of Virginia. (Dan Addison/University of Virginia)

The University of Virginia, facing pressure from lawmakers to contain prices and enroll more Virginians, will open its gates a bit wider to in-state students in the next school year and offer some middle-class families a new tuition break worth $2,000 a year.

The public flagship university’s governing Board of Visitors approved a resolution Tuesday afternoon that aims to add 100 undergraduate seats for Virginians and create scholarships for students whose families live in the state and earn less than $125,000 a year.

The expansion of in-state enrollment represents a modest increase from the current total of roughly 11,000. The in-state share of undergraduates, about 69 percent, will be virtually unchanged.

The number of Virginians the university enrolls has grown significantly in this century as the school in Charlottesville has grown. The projected total for in-state students in the coming school year, including growth in the number of first-year and transfer students, is up 28 percent since 2001.

“Our strategy for access and affordability keeps U-Va. on a sustainable financial path that increases quality, opens our doors wider to Virginians and cements our commitment to fully meet the needs of admitted students without any pre-screening of their family financial situation,” President Teresa A. Sullivan said in a statement.

Tuition and fees for Virginians this school year total about $15,700, not counting room and board. The in-state price has risen significantly in recent years. But it is still far lower than tuition at comparably ranked private universities. Tuition and fees for out-of-state students totals more than $45,000. The out-of-state premium is crucial to U-Va.’s finances.

U-Va. is one of a small group of schools that admit students without regard to financial need and pledges to meet full need. Under U-Va.’s plan, officials said, the “Cornerstone Grant” would be available to students from certain families with annual income of less than $125,000 who might not now qualify for need-based grants. The grants would be worth as much as $2,000 for first- and second-year students and up to $1,000 for third-year students.

During the next three school years, the new scholarships and additional seats for Virginians are expected to cost $15 million. The money will come from income generated by more than $2 billion in reserves U-Va. set aside last year for strategic investments. That reserve fund drew criticism from some state lawmakers, who wondered how U-Va. had been able to accumulate so much cash outside of its endowment.

Del. David B. Albo (R-Fairfax), who graduated in U-Va.’s Class of 1984, is sponsoring a bill that would, among its provisions, require U-Va. and most other public universities to enroll at least 75 percent of their students from within Virginia.

“My citizens want two things: affordable tuition and access,” Albo said. “None of them cares if U-Va. is No. 1 if they can’t get in.”

U-Va. is not the only school that would be affected. The in-state-student share is 66 percent at the College of William & Mary, 72.5 percent at Virginia Tech and 74.5 percent at James Madison University, state data show.

Albo’s bill faces uncertain prospects in the Republican-controlled legislature because public universities wield significant clout in Richmond. Sullivan declined to comment on Albo’s bill.

Brian Whitson, a William & Mary spokesman, said the highly regarded school in Williamsburg opposes the bill. “Out-of-state students bring a diversity of backgrounds, experience and perspective that you expect to find at a national university,” Whitson said.