Reagan administration officials have ordered St. Elizabeths Hospital to fire 653 employes by Dec. 1 in order to stay within its $118 million budget for next year.

In a memo received Tuesday, the federal psychiatric hospital in Southeast Washington was given until Friday to devise proposals on how to fire 653 of its 3,900 employes. The memo's author, Robert Trachtenberg, deputy administrator for the federal Alcohol, Drug Abuse and Mental Health Administration, asked that entire departments be cut, including programs aimed at Hispanics, the deaf, adolescents and children, rather than an across-the-board reduction in hospital staff.

"A 15 percent reduction for everyone takes the pain away equally, but it is not an effective way of dealing with what departments should be cut," Trachtenberg said in an interview yesterday.

The memo is the latest in the federal government's attempts to withdraw support for St. Elizabeths Hospital and to encourage an unwilling D.C. government to assume responsibility for the hospital. The majority of its patients are District residents, but federal patients, such as illegal aliens, military people and mentally ill patients ordered there by federal courts, also use the facility.

"We're looking for an ultimate agreement that the D.C. government will take it over," said Trachtenberg. "This is our second step in a 10-year phasedown for District takeover."

The first step has been a cut in federal financial support. The coming fiscal year is the third year that the president and the Office of Management and Budget have asked for reduced budgets for the hospital, which is supported by federal and D.C. taxpayers. In past years, Congress has added extra money to continue the hospital's operations. However, for the 1984 fiscal year, which begins Oct. 1, nobody has come forward to make up the hospital's $25 million deficit.

"The hospital is still the federal government's responsibility," said Betsy Reveal, the D.C. budget director, who noted that the District is giving the hospital $29 million in the coming year. "I'm quite certain that kind of RIF reduction in force is going to be difficult politically."

Dr. William Dobbs, 59, superintendent of St. Elizabeths, said through a spokesman that he would have no comment on the requested firings. The spokesman, Harold Thomas, said the hospital is following orders. "We are a part of the administration. We're working with a number of contingency plans." Thomas confirmed that Dobbs, who has said he will retire soon, will be "stepping down" on Oct. 1.

Officials from the American Federation of State, County and Municipal Employees, who represent many of the hospital's workers, could not be reached for comment yesterday.

The memo asks that programs be "reduced, abolished or consolidated" and specifically suggests that the hospital end its program for caring for physically ill patients, its alcohol and drug-abuse programs, its mental health program for the deaf and a day-care mental health program for Spanish-speaking patients.

Federal authorities also asked the hospital to explain in detail how the loss of programs would affect patients, as well as the hospital's accreditation.

Several doctors and social workers at the hospital decried the cuts yesterday, saying there is no other place in the community where these services are offered. All refused to be quoted by name, saying they fear retaliation by administration officials.

"This would eliminate model programs," said one psychologist. "The mental health program for the deaf is unique, one of the few where all the doctors, nurses, everyone can speak in sign language."

Trachtenberg said the cuts, although painful, are unavoidable. "We can't sit here with not enough money to cover its staff. No one has any choice." He said the hospital must look for new homes for some people who don't belong there, as well as delay purchases and planned construction in order to keep within its budget.

The reductions also are aimed at trimming the number of patients at the hospital, Trachtenberg said. Currently there are 1,800 inpatients and 3,000 outpatients, according to Thomas, the hospital spokesman. Trachtenberg said the administration would like to reduce the population to between 1,000 and 1,200 inpatients.