The D.C. Board of Education, responding to a request from city officials, reduced its fiscal 1984-89 capital improvements budget proposal yesterday by $16.5 million and said it will consider further cuts.

The board already had received approval from the city for $61.5 million in capital improvements that ranged from $10.2 million to modernize Coolidge High to $556,200 for various boiler replacements. This summer, the board submitted a request to add $75.5 million to the five-year plan for further improvements.

The city's Office of Planning and Development recommended to Mayor Marion Barry recently that the school system receive only $27.4 million of that request, according to a report Superintendent Floretta D. McKenzie gave the board at a special meeting yesterday.

In addition, she told the board, the city says it has a backlog of $548 million in unfunded capital projects, and has asked the board to study its previously approved $61.5 million budget "to identify projects which can be canceled, deferred or reduced in scope and cost."

City Budget Director Gladys Mack confirmed yesterday that the city had asked for cuts in the schools' capital budget. "We are concerned about completing projects already in the pipeline and limiting new requests until we can clear the backlog," she said.

McKenzie said if the $75.5 million request is cut as severely as the planning office has proposed, needed school renovations will be hampered.

"The physical condition of school facilities is deplorable enough that improvements cannot be deferred substantially," said McKenzie. "In addition, by not including projects at this time, improvements may be deferred until 1990, which would be disastrous."

The board trimmed its request to $59 million by changing the procedure in which it orders capital improvements--looking at priority measures like roof replacements and science lab renovations on a city-wide rather than school-by-school basis.

Under the changed request, roof replacements at schools around the city have the highest priority, at an expected cost of $6.3 million. Just over $7 million is budgeted for conversions of empty classrooms to other uses, and $11 million is requested for electrical modernizations.

Board President David Eaton said yesterday the board could not reduce its supplemental budget request further than that, but the board approved a motion to tell the city that it will look at canceling or reducing other improvements projects previously approved.

"I know we don't live in a perfect world," said Eaton. "We are willing to work with the administration and the City Council in reducing these requests, but we will fight for those that we feel are essential."

In other action, the board voted funds for the rest of this school year for the Multicultural Career Internship Program, a school designed to provide career assistance and intensive English instruction to recent immigrants.

MCIP was formed in May 1979 and had been funded by the Department of Labor, but federal budget cuts left it without operating funds for the current school year. A working agreement with the schools has allowed the facility to operate in the city's Lincoln Junior High School at 15th and Irving streets NW. Graduating students received a D.C. schools diploma, but the board of education had never before offered funds to operate the program.