Prince George's Executive Parris Glendening sent an amended $538.5 million budget to the County Council yesterday that adds $10.2 million to his original projections for fiscal 1984 and averts all proposed layoffs of county employes.

Glendening's original budget, submitted March 31, called for the layoffs of 412 county employes, including teachers, police officers and firefighters, as well as a hiring freeze in virtually all departments. Glendening had said the layoffs were necessary to submit a balanced budget as required by law, but promised to restore personnel if more money became available.

"We are still in a position of fiscal difficulty and uncertainty," Glendening cautioned yesterday, "because the sources of the additional money are inadequate for the county's long-term needs."

According to budget director Robert Duncan, most of the additional revenue, about $7.1 million, is money the county will receive during the year from Lotto, a lottery game approved by the General Assembly this month. The game is scheduled to begin in November, and will run for one year.

An additional $2.2 million is expected to come from the lease of the county's three hospitals to a private, nonprofit firm, scheduled to take effect July 1. The county will receive an increase of $265,000 in state aid for its 911 emergency number program, and another $632,000 will come from recalculations in state aid to education.

In addition to filling the threatened positions, Glendening also recommended funding to replace aging police cars, ambulances, dump trucks, fire equipment and computer equipment.

Reaction to the amended proposal, which must be ratified by the council by June 1, was mixed. Department heads and union leaders expressed relief that firings were avoided, but were disappointed that more money to fill vacancies and purchase more equipment was not available.

"Yes we're happy, but we're still short," said school spokesman Brian Porter.

Porter said the $310 million proposed for the schools, $3.8 million more than this fiscal year's school budget but about $6 million less than the school board requested, does not provide for the replacement of worn textbooks or reduction in class size.