Department heads of the financially strapped District of Columbia government were ordered yesterday to prepare for additional cuts in their bugets and programs during the coming fiscal year.

City Budget Director Gladys W. Mack sent instructions to all agencies, telling them to propose reductions within the next two weeks that would permit essential city services to be maintained.

The purpose, she said, is to absorb inflationary cost increases in such areas as energy, building rentals, supplies and payrolls without increasing the size of the proposed $1.5 billion operating budget.

Mack sent each agency an estimated goal for its reduction. However, she refused to release a list showing how the cuts would affect city departments.

The reductions would apply to the 1981 fiscal year that starts Oct. 1. They would be similar in their effect to $26 million in cuts ordered by Mayor Marion Barry in his cost-reduction program for the current 1980 fiscal year, part of an effort to avert a deficit of up to $172 million. The current program includes the elimination of 1,223 city jobs by layoffs and atrition.

In her directive, Mack raised the possibility of more layoffs during the coming fiscal year to meet cost-reduction targets, but did not suggest them. She said financial benefits of the cuts made for this year should be carried over into 1981.

Hearings on the 1981 budget are under way in Congress. Mack said the new departmental reduction plans would be the basis for proposing 1981 budget amendments to Congress.

In another development, City Administrtor Elijah B. Rogers said a possible consolidation of three city departments as an economy move is being explored by a task force.

Rogers said a study is being made of the Departments of General Services, Environmental Services and Transportation to see if overlapping functions could be eliminated by merging them into a single public works department. No decision has been reached, he said.