The University of Virginia’s governing board approved a 4.3 percent increase in tuition and fees Wednesday for first-year in-state students, overwhelmingly supporting the price hike despite objections from critics who called it excessive.

The increase, to $12,998 a year beginning in the fall, was approved on a 12 to 3 vote of the Board of Visitors in a meeting held in Abingdon in Southwest Virginia, according to a university spokesman. The dissenters were board members Helen E. Dragas, Marvin W. Gilliam Jr. and Edward D. Miller.

Miller said last week that it is hard to justify the rate increase when the national inflation rate is about 1.5 percent. Although he was certain that the increase would pass, he said it was important for U-Va. and other universities to contain costs: “Higher education needs to get a grip on this,” he said.

Last year, the board approved a 3.8 percent increase in tuition and fees for Virginians. Debate has intensified over U-Va.’s pricing policy, with some members complaining that the increases are saddling students with more and more debt.

But supporters say the increase will help the prestigious public flagship university increase faculty and staff pay and take other steps to remain competitive.

“Our efforts focus on strategic initiatives that further strengthen one of the country’s best public research institutions,” U-Va. Rector George Keith Martin said in a statement. As rector, Martin is head of the board.

Dragas, a former rector, has previously voiced skepticism about tuition increases. Last year, when university leaders proposed a four-year plan for the school’s finances that included regular tuition increases of 3 percent to 4 percent, Dragas said that such increases could make the state school inaccessible to many Virginia families. She also voted against last year’s 3.8 percent increase, saying afterward that “we cannot stay on an unsustainable tuition increase path.”

School administrators have argued that an era of declining state funding have made increases necessary.

U-Va., like other top public universities, has shifted some of the tuition burden to out-of-state students. On Wednesday, the board also raised undergraduate tuition and fees for out-of-state residents by 5.9 percent, to $42,184 in the coming year — more than three times the in-state price.

The tuition and fees approved for the 2014-15 school year do not include charges for room and board and other expenses.