The University of Massachusetts Board of Trustees approved a 4.9 percent increase in student fees today, giving its emphatic blessing to a proposal Governor Deval Patrick had slammed the day before in a last-minute letter and phone call to UMass President Robert Caret.

The hike in the cost of attendance is not unusual — UMass has raised its fees for at least 10 consecutive years — nor is it above the average for that period, which clocks in around 5 percent.

The new increase, which affects all undergraduates and most graduate students, is also smaller than recent fee hikes at several other state universities and UMass peer systems. It would raise the fees for in-state undergraduates by about $580, making annual tuition and fees $12,481. The cost of room and board varies on the campuses; it’s about $10,000 at the Amherst flagship.

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Those numbers had left many UMass officials, who voted 15-2 in favor of the proposal, believing the increase would not be controversial.

But Tuesday morning, Patrick weighed in unexpectedly, telling Caret he believed any rise in fees would put too much pressure on students and families, especially given that student loan interest rates are set to double if a deadlocked Congress does not stop them from doing so. He said he believed UMass first needed to ensure it had cut all possible costs.

Patrick said this morning at the State House that it’s “a crummy time” to raise fees.

“I mean, I get the economic piece, the financial piece. I’ve seen the numbers. I’ve been briefed,” he said of the university’s financial predicament, noting that he hoped the state would increase support for higher education before the end of his term. But he added that “quid pro quo for that is to show the public that every element of waste, every dime, has been wrenched out, where it can be.”

Several UMass board members said they believed Patrick’s attempted intervention was designed to put the governor squarely on President Obama’s side in the national debate on college affordability. They noted that he did not personally lobby UMass trustees to mobilize them against the hike, suggesting he might have come out against the increase largely for public relations purposes.

But on Wednesday, an administration official said Patrick had made his intentions clear to UMass months ago, before the national affordability debate heated up.

“The governor was very clear during a lunch in March with Caret that he did not want to see any student fee increases,” she said. “We wanted the increase to be zero. The idea that this is coming as a surprise to anyone at UMass is ridiculous.”

On Tuesday night, the UMass board finance committee met to consider the fee increase and added an amendment that could address a recent and precipitous drop in state funding – and put the ball back in Patrick’s court. Board chairman James Karam proposed that the university freeze the new fee rate for the next two years, on one condition: that the state restore its funding to 2009 levels, allowing UMass to get half its revenue from the state and the other half from students.

Karam noted that a two-year freeze would be unprecedented nationwide for a public university system, and called it “a hell of a commitment from the university.”

If the state agrees, it could signal as much in ongoing budget negotiations. Patrick has proposed a 6 percent increase in funding to UMass, but it is not enough to constitute the 50-50 split Karam and Caret are seeking. Instead, according to UMass, the state’s share is expected to dip next year from 45 to 43 percent.

“We need to get back to a footing where the state is funding its public university at some reasonable level, at least equal to what students and their parents are paying,” Caret said Wednesday in a statement. “To do otherwise is to take the ‘public’ out of public higher education.”

At Wednesday’s board meeting, state secretary of education Paul Reville — acting on Patrick’s explicit instructions — argued against the fee increase, suggesting that UMass instead undertake a study to examine ways it might cut costs.

The UMass board also voted Wednesday to expand an existing task force on efficiencies and asked it to report back on “findings and strategies for achieving cost savings.”

But university officials said they are already aggressively cutting costs because the state has stripped back the system’s funding. In the last three years the university has cut 645 jobs, saving $68 million, and 160 more positions are on the chopping block for another $17.4 million.

The system recently has taken on additional financial responsibilities. Enrollment has grown by 12,000 in the last 10 years; research expenditures have jumped $100 million in the last four; and labor expenses have risen this year due to new union contract obligations. UMass is also facing a $3.2 billion backlog in deferred maintenance.

The new fee increase would net the system some $25 million in revenue.

Without that money, said Karam, the university might have to consider cutting projects that Patrick and others have praised as key to the state’s economic recovery.

“We could eliminate more of what we’re doing. We could eliminate things like funding for the new green high-performance computing center” in the struggling Pioneer Valley, Karam said. “But if we did that I’m not sure what we’d be providing to the public.”