The state Board of Regents is threatening to prevent up to 2,800 students from attending Utah colleges next fall because of budget woes.

In a letter to the Legislature on Friday, the regents said the enrollment crisis has arrived and the state's higher education system can no longer, year after year, absorb more students without more state funds.The regents, the governing body of state colleges and universities, said enrollment restrictions will go into effect next fall if legislators settle on an increase of only $22.8 million in state funding, which is now being considered.In the past few years, the regents have anticipated and warned about possible enrollment restrictions as the students who have crowded the public-education classrooms moved onto college campuses. Friday's letter, however, is the first time they actually have said that access to the state's nine colleges and universities would be restricted without a certain funding level.

The proposed $22.8 million increase for school year 1991-92 over this year's budget includes about $11 million for enrollment growth, which is only 49 percent of the $24.9 million that higher education officials believe will be needed to handle a projected increase of 6,551 new students next fall.

The state appropriated $295 million for 1990-91 to run its higher education institutions.

"On this short notice, we cannot authoritatively say what the specific impact will be, but we would estimate that up to 2,800 students will not be able to attend next fall at the $22.8 million funding level. These are students who are qualified and prepared under our current system of enrollment management," the letter says.

The regents want legislators to approve a higher-education funding increase of $25.6 million - an amount significantly below the regents' original request of $68.7 million but one with which higher education officials say they will make do. That proposed $25.6 million includes $16.5 million for enrollment growth, which would cover about 78 percent of the projected student increase or 5,117 new students.

Despite the letter, it doesn't look good at the Capitol for more enrollment money.

The regents adjourned early so they could hand carry their letter to the Joint Higher Education Appropriations Subcommittee. The subcommittee, based on budget agreements reached in legislative caucuses Friday, decided to recommend the $22.8 million increase for higher education to the Executive Appropriations Committee. That recommendation went to the committee late Friday.

The subcommittee's Senate co-chairman, Dix McMullin, R-South Jordan, said the subcommittee was instructed to also prepare the second higher budget with the $25.6 million increase, but that one could only be used after Sept. 1 - a few weeks before school starts - if the revenue becomes available.

Commissioner of Higher Education Wm. Rolfe Kerr said if the final increase in funding, when the Legislature finishes next week, is the lower $22.8 million, the regents will begin immediately to plan the enrollment limitations.

The regents already have a task force studying enrollment growth and developing a long-range plan for managing it. Regent Michael Leavitt, a task force member, said the task force would accelerate its work, deciding enrollment-restriction strategies for next fall and beyond.

The specific strategies to restrict enrollment have not been decided. The letter makes no mention of any methods. Possibilities, however, could be new entrance requirements and higher tuition.

The letter did warn legislators what enrollment restrictions will mean to them and the regents personally. In the next few years, it said, "both the Legislature and the Board of Regents will be contacted continually by students and parents frustrated by their inability to gain the level of access to which they have become accustomed."