State funding for the University of Alaska would be cut $70 million over three years under a deal Gov. Michael J. Dunleavy (R) approved Tuesday that appeared to pull the higher education system back from the brink of immediate fiscal crisis.

Previously, Dunleavy had demanded a $135 million budget cut for the university, to be enacted in one year. That would have represented a reduction of about 40 percent, raising existential questions for the university’s campuses in Fairbanks, Anchorage and Juneau.

The proposal sent shock waves nationally as a signal of an intensifying and often partisan debate over state support for public higher education.

Now, Dunleavy is backing a funding cut for the Alaska system that is still quite deep but would occur in three stages: $25 million in the 2020 fiscal year, then another $25 million in 2021, then $20 million in 2022. Cumulatively, the cuts would reduce state funding about 20 percent.

“My intention was never to cause angst,” Dunleavy said in a televised news conference from Anchorage after he signed a fiscal agreement with the university system’s board chairman, John M. Davies. “My intention was to close this budget gap as much as possible. … We have to be serious about this.”

University officials said the slower pace of reductions would give them time to restructure. They predicted some layoffs, but fewer than they had feared a few weeks ago.

“There’s no great state without a great university — period,” University of Alaska President James R. Johnsen said at the news conference. “This is an opportunity to pivot to the positive.” He pledged to concentrate cuts as much as possible on administrative expenses, seeking to preserve resources for academics and student services.

The system has about 26,600 students. Controversy erupted this summer after lawmakers failed to overturn vetoes by Dunleavy that slashed education funding. Dunleavy, elected last year, took office after campaigning on a pledge to give state residents a higher dividend from a reserve fund created through the state’s oil wealth.

Dunleavy said the education system needed to be restructured to help the state live within its means. Critics said the higher education cuts the governor backed would harm the state’s economy.