The budget cuts that the Reagan administration wants to make in Comprehensive Employment and Training Act (CETA) personnel, announced in detail yesterday, will require the District to fire about 1,000 people, and Montgomery County to lay off 160, local officials said yesterday.

"It's going to have a devastating impact, obviously, on the city," said D.C. City Administrator Elijah B. Rogers. "You're talking about 1,000 workers and a lot of them are providing direct services to citizens. It will mean delays, longer lines, more complaints."

Officials in Prince George's, Fairfax and Loudoun counties, as well as Arlington and Alexandria, said yesterday they have not had a chance to calculate the impact of the cuts on their CETA public service programs.

While the U.S. Department of Labor said that a number of agencies wil be involved in trying to find jobs in the private sector for those laid off, city officials expressed doubt this could be done.

"The economy is down; I don't see where these people are going to wind up getting jobs," said Ivanhoe Donaldson, director of the city's Department of Employment Services. "It means a lot of people are going to be going on the unemployment lines. It means more pain of the street."

Federal officials have pointed out that the purpose of CETA was to provide jobs and training, not a permanent federally funded work force for local governments.

Jack Hashien, a spokesman for the Labor Department, said the government will ask chambers of commerce, major community-based groups, and others to help find jobs for the ex-CETA employes in the private market. "To say there are no jobs and these people are going on welfare is overstating it a bit," Hashien said. "The jobs are there."

The cuts announced yesterday amounted to a 36 percent reduction in federal funds to localities for CETA public service jobs. The two programs affected are Title II(d), which provides on-the-job and classroom training for the hard to employ, and Title VI, which provides jobs and training for those unemployed because of a downward economic cycle. The jobs are generally low-paying clerical positions in local government and community-based organizations.

The Title VI cuts have to be approved by Congress. The others do not need additional approval.

The cuts, which come about halfway through the fiscal year, mean that some localities will have to terminate employes immediately because they have been spending based on higher projections. "We are now alloted $1.7 million for our II(d) program, and we've already spent $1.6 million," Rogers said.

Donaldson said that the 400 employes in the city's Title VI program will have to be released within a month, and that the 600 in the Title II(d) program will probably be gone by the middle of the summer.

Alan Kutz, Mongtomery County's CETA chief, said the 160 employes that fall in those categories in his county wil be terminated within about three months.