Tuition will climb an average $233 this fall at Minnesota’s seven state universities, to just over $7,000 a year, under a budget plan approved Wednesday by the board of trustees.

It’s the first tuition hike at the four-year state universities since 2012, when tuition was frozen under a deal with state lawmakers.

Chancellor Steven Rosenstone formally proposed what he called the “modest increase,” which averages 3.4 percent, after the Legislature balked at his request to fund a full tuition freeze.

But Rosenstone noted that the budget approved Wednesday contained good news for the majority of students at the Minnesota State Colleges and Universities system (MnSCU).

It freezes tuition at the system’s 24 community and technical colleges for another year, as mandated by the Legislature. The average rate, $4,816 a year for a full-time student, has not changed since 2012.

And at the state universities, low-income students won’t feel the impact of the proposed tuition increase, he said, because it will be offset by increases in state and federal grants.

“The glass is about 80 percent full here on the tuition front,” Rosenstone said.

Rosenstone noted that the student associations at most of the state universities supported his decision to recommend an increase in tuition. “None of them said, ‘We’re excited about proposing a tuition increase,’ ” he said. But they preferred it to program cuts. “They don’t want to lose faculty, don’t want to lose academic advisers, don’t want to see programs closing.”

Rosenstone had asked the Legislature for $142 million in extra funds to freeze tuition for all MnSCU students for the next two years. In May, lawmakers approved only part of the request, $100 million, leaving the system with a funding gap.

Under the legislation, the state universities will not be able to raise tuition again in the 2016-17 school year. So this year’s increase will have to cover a two-year period, Rosenstone said.

The two-year colleges will be required to cut tuition by 1 percent next year.

Meanwhile, the regents of the University of Minnesota system are considering a 1.5 percent tuition increase for state undergraduates that would raise their sticker price at the Twin Cities campus by $180 to $12,240. University officials offered to extend the tuition freeze for two more years in return for a $65 million increase in state funds, but lawmakers approved only $22 million for tuition relief over the next two years.