George Mason University's trustees took the first tentative step yesterday toward establishing a branch in Prince William County by voting to authorize planning a "presence" there despite warnings that it could weaken the main campus.

Board Chairman Hector Alcalde also named a committee to study whether the Fairfax County school should establish "some sort of health complex." The university has a law school, business school and nursing program, but no medical school, an idea that President George W. Johnson has opposed as too much work for a young university to take on.

Yesterday's Prince William vote authorized Johnson to ask the state Council of Higher Education, an advisory group to the state legislature, for permission to study the proposal. The council's director, Gordon Davies, has proposed a new university for Northern Virginia and rejected the idea of a branch campus as inferior.

Discussion so far has centered on establishing a branch on the grounds of Northern Virginia Community College in Manassas that would offer a limited number of classes in engineering and business. A tentative timetable calls for a trustees vote next spring, a proposal to the Virginia General Assembly in early 1989, and start-up that fall.

The Manassas branch would be the third campus for the university, which has a main campus south of Fairfax City and a law school in Arlington. George Mason, the fastest-growing state-supported school in Virginia, also is studying the feasibility of expansion to Leesburg, Stafford County and other parts of Northern Virginia.

Supporters of the Prince William campus argue that it meets a demand for more technical education in the area, particularly from employes of rapidly growing high-technology companies.

"Why should we give up our territorial rights without a look-see?" asked Trustee Myron P. Erkiletian. He said the Prince William campus would be part of George Mason's efforts to be "responsive to the region."

But Randolph W. Church Jr., one of two trustees to reject the proposal during the voice vote, said it could lead to "fragmentation of the undergraduate effort" in Fairfax if Prince William students were siphoned off to a new campus.

Church criticized the "Mount Everest syndrome" under which university officials say they must meet all needs. He also opposed spending university money to build on a site the university does not own.

In naming a trustee committee to study a health complex, Alcalde said, "What's more important than health services? And we as a university would totally ignore {it}? I think we ought to look at it."

No opposition to the idea was voiced by board members, although Alcalde said he realized some were skeptical. Asked whether he continues to oppose a medical school, Johnson said "there is some justice" in the argument that if a Prince William branch campus can be tentatively discussed, so can a medical school.