The director of the federal agency that monitors St. Elizabeths Hospital told administrators of the hospital yesterday he will ask Congress for $11 million more for the hospital, a move that could reduce planned layoffs of 906 employes to 200 to 300.

The statement by Dr. William Mayer, director of the Alcohol, Drug Abuse and Mental Health Administration, reverses the Reagan administration's position of refusing to ask for more support for St. Elizabeths, which faces a $25 million deficit.

Mayer's remarks were made at a meeting of the hospital's clinical directors and were related by several sources. Mayer's office would say only his meeting with the hospital administrators "was an announcement to them."

In a congressional hearing in August, Mayer said his department would not ask Congress for more money and said the deficit should be made up by the District. The reduced federal support for St. Elizabeths is part of the government's 10-year program of transferring full responsibility for the mental hospital to the District.

Under the plan discussed by Mayer, the extra $11 million would allow the hospital to keep its hard-won accreditation.

After hospital superintendent Dr. William Dobbs prepared the plans for the reductions in force and program cuts, which Mayer had requested, he said the reductions would cause the hospital to lose its accreditation. This would prompt a further loss of funds because insurers and several government programs will not reimburse services performed in unapproved hospitals.

Under Mayer's new plan, which was developed by a committee of health professionals at St. Elizabeths, the hospital would still lose 40 alcohol and drug abuse beds and one of two mental health wards for the deaf. Training throughout the hospital would be cut by 15 percent. But the large staff cuts that are set to begin Dec. 1 would be eased.

"It's moving in the right direction," Lillian Secundy, president of the Mental Health Association of the District of Columbia, said of the $11 million request. "We're still looking toward getting the $25 million so that we won't have to cut any patient programs."

According to sources at the meeting, Mayer also announced that Dr. Scott Nelson, currently the mental health commissioner for Pennsylvania, will become the new superintendent of St. Elizabeths Hospital.

The health officials were told that Nelson, head of the Pennsylvania Office of Mental Health, will assume his new duties Oct. 1. Current superintendent Dobbs, a veteran of 27 years at the hospital, has long-announced plans to step down and will be joining the staff of the National Institute of Mental Health in Rockville.

James Helsing, a spokesman for Mayer's department, said there was "no official announcement" of Nelson's appointment.

Nelson came to Pennsylvania after holding a similar post in New Mexico. He made news when he publicized a report in 1980 that found that low salaries had forced Pennsylvania's 18 state mental hospitals to hire psychiatrists who have mental or physical problems or who speak poor English.

A spokesman for Nelson in Harrisburg, Pa., said, "Given the personnel situation, he's not free to make any comments at this time."