BERKELEY (CBS / CNN) — Most of the more than 770,000 students at California’s two main university systems, which include several Bay Area campuses, aren’t likely to return to campus this fall.

The California State University system, which claims to be the nation’s biggest four-year university system, plans to cancel nearly all in-person classes through the fall semester to reduce spread of the coronavirus, Chancellor Timothy White said Tuesday at a board of trustees meeting.

READ MORE: 4.3 Magnitude Earthquake Strikes Near Los Angeles

At the University of California, which has 10 campuses across the state, “it’s likely none of our campuses will fully re-open in fall,” Stett Holbrook, a spokesperson for UC, told CNN in an email.

Dr. Anthony Fauci, a key member of the White House’s coronavirus task force, told Congress on Tuesday that it is a “bridge too far” for schools to expect a vaccine or widely available treatment for Covid-19 by fall reopening time.

“First and foremost is the health, safety and welfare of our students, faculty and staff, and the evolving data surrounding the progression of Covid-19 — current and as forecast throughout the 2020-21 academic year,” White said in making his announcement.

Potential exceptions at CSU may include nursing students who need clinical training to be on track to get licensed to work in health care, White said, or students who need access to equipment for their training.

Students who need to continue research in labs will also continue forward under rigorous safety standards. White said students may need to work in shifts, wearing personal protective gear.

Rigorous health and safety requirements will be in place, such as sanitizing and spreading students out. Instead of 15 students per class, it may be five students, he suggested.

Some of CSU’s 23 campuses, which include San Jose State, San Francisco State, CSU East Bay and Sonoma State in the Bay Area, may continue to offer remote learning only.

“On some campuses and in some academic disciplines course offerings are likely to be exclusively virtual,” White said.

University of California “will be exploring a mixed approach with some material delivered in classroom and labs settings while other classes will continue to be online,” Holbrook said.

California was the first state to issue a statewide stay-at-home order, effective March 19. Like many other schools, colleges and universities across the nation, UC and CSU began suspending in-class learning in March.

READ MORE: San Francisco Mayor Defends Criticism After Video Catches Her Dancing Maskless at Night Club

Some universities will resume classes

Around the country, most other colleges and universities are still trying to figure out what instruction will look like in the fall, with some saying a decision will be made later.

Universities in at least six states have said they expect to hold classes on campuses in the fall: the University of Alabama; the University of North Carolina System; Texas Tech University; the University of Tennessee; the nine-campus University of Louisiana system; and Morgan State University in Maryland.

The North Dakota State Board of Higher Education last month voted unanimously in favor of a motion supporting the return of students to campuses in the fall

Harvard said last month it will be open for the fall semester, but some or all instruction may continue to be online.

Schools from grades K-12 are closed in 48 states for the remainder of the academic school year, which ends in the next few weeks for many.

Los Angeles Mayor Eric Garcetti told CNN’s Anderson Cooper on Tuesday that he supports CSU’s decision to cancel nearly all in-person classes for the fall semester.

“I absolutely think it’ll be a different school than we’re used to, whether that’s fewer days a week, whether it’s half the class coming in, whether it’s new spaces or places where we educate,” said Mayor Garcetti.

Garcetti said K-12 schools in Los Angeles should prepare to resume with online classes, but “it would be a pity if we have all of our children only online throughout the rest of this calendar year.”

Garcetti suggested finding safe ways for kids to be at school as long as the numbers are stable.

“We should figure out safe ways for kids to be there, at least some of the week, face to face with teachers, with their peers,” he said.

MORE NEWS: COVID: San Mateo County Mounts Effort to Boost Coastal Town Vaccination Rates

© Copyright 2020 CBS Broadcasting Inc. All Rights Reserved. This material may not be published, broadcast, rewritten. CNN contributed to this report.