Cost-of-living increases for Prince William County government employees will be eliminated and hiring for all nonessential jobs has been frozen to cope with a larger-than-expected budget shortfall, County Executive James H. Mullen announced yesterday.

Even with those measures, officials said, the Board of County Supervisors probably will have to cut an additional $9 million from the $160 million government budget for fiscal 1992, which begins in July 1991. Officials said the cuts announced yesterday will save about $7 million.

Prince William's public schools also are likely to hold positions open and limit raises, benefits and supply costs, said Superintendent Edward L. Kelly. The school system will get $8 million less from the county, a reduction of 5 percent, in 1992. State reductions will be announced next week.

"We're not looking to massive cuts. It's only how to limit growth," Kelly said.

Prince William's cuts are the latest in a series of budget-cutting announcements from local governments in the Washington area.

In Prince William, 204 of 2,500 staff positions are vacant, but 20 of them will not be affected by the freeze because they are fire and police officers or are mandated by the state, said personnel director Cleil Fitzwater. Any other nonessential personnel who retire or resign will not be replaced.

"Most vacant positions will be eliminated in the '92 budget," Mullen said.