A group of Mayor Marion Barry's senior aides gathered Tuesday night in the spacious office of City Administrator Thomas M. Downs to confront the latest crisis in the District's troubled ambulance service.

Another city resident had died amid reports of a bungled ambulance run. As frustrations grew, according to sources, there were angry suggestions that Barry get rid of Fire Chief Theodore R. Coleman, blamed for several public embarrassments involving the ambulance service and the Fire Department.

When Barry went before reporters Wednesday morning, a city official said the mayor's office kept Coleman away from the news conference. Barry, who has assigned several top aides to try to help Coleman over the years, refuses to comment on Coleman's performance.

But Coleman still has his job.

Despite severe criticism of the fire chief's performance and Coleman's apparent inability to get along with his new ambulance chief, the mayor's most senior advisers say Barry is unlikely to replace Coleman any time soon. The reasons, they say, are a complex mixture of personal, racial and political considerations that have little to do with Coleman's actual performance in a job that pays about $70,000 a year.

Barry, the aides said, always has been reluctant to fire anyone and feels that problems within the ambulance service are longstanding and not solely attributable to Coleman's management. He also has told several of his advisers that he does not want to force Coleman to retire because the departure of Coleman, who is black, would be seen as a victory for the firefighters union, whose most visible leaders are white.

Aides say Barry fears the dismissal of Coleman -- whose rise to the top of a department that once was segregated and still is beset with racial tension and affirmative action lawsuits -- would result in criticism from some segments of the city's black community that could be more damaging to the mayor than allowing Coleman to stay a while longer.

At the start of Barry's third term last year, according to city officials, Barry reached agreement with Coleman that he could stay through August of this year, when Coleman is to be the first black fire chief to preside over a meeting in Washington of the International Association of Fire Chiefs.

Coleman did not return telephone calls to his office yesterday. Barry, through press secretary John C. White, said "no comment" when asked if Coleman had the mayor's confidence.

Thomas Tippett, president of Local 36 of the Firefighters Association, which represents the city's approximately 1,300 firefighters, said yesterday that Barry also has told the union that Coleman would stay until the fire chiefs' convention.

Tippett sharply disputed characterizations of his union as white-dominated, saying many of the union's leadership's positions are held by blacks.

"Fifteen years ago they could use {that criticism}, but that's out," Tippett said. Tippett said many firefighters, black and white, don't understand why Barry has not told Coleman to retire.

Tippett said the union, which initially supported Coleman's appointment as chief in 1983, has purposely refrained from calling for his ouster because the union believes that would only make Barry "dig in his heels." Instead, Tippett said the union has concentrated on highlighting "problems with upper management."

In the past few years, Coleman has been criticized on a wide range of issues, including allegations of poor training of paramedics and rescue divers, and the use of faulty equipment. There have been personally embarrassing episodes, including ordering firefighters to dig his car out of the snow last year and to repaint new fire trucks last summer.

More seriously, critics charge neglect of the ambulance service.

Since 1986, there have nine reported incidents of people dying after ambulances were slow to reach them, although no official link has been made between the deaths and the delays. On Sunday, a Northeast man died at D.C. General Hospital. An ambulance dispatched to the victim's home took 40 minutes to arrive and officials later said the ambulance crew was lost.

Barry has tried numerous strategies to solve such problems.

He commissioned a task force in 1986 on ambulance service, but critics say little was done with its recommendations.

In an effort to ease tensions within the fire and ambulance units, an aide said Barry assigned longtime adviser Joseph P. Yeldell, director of the Office of Emergency Preparedness, to "keep tabs on Coleman." Yeldell has met frequently -- as often as weekly -- with union leaders within the fire and ambulance divisions, Tippett and others said. Yeldell has declined to comment on his role.

Dr. Reed V. Tuckson, the city's public health commissioner, also has played a major role in trying to improve the ambulance service. Tuckson, who was appointed by Barry to monitor the ambulance service for six months during 1987, is due to report next week on Sunday's ambulance errors. Seven emergency service employees have been placed on temporary administrative leave with pay in connection with that incident.

The most recent efforts to improve the crisis-ridden ambulance service have been hampered because John M. Cavenagh, who became ambulance director in October after a five-month national search, has not received Coleman's cooperation, according to Fire Department and medical officials who were interviewed this week.

Cavenagh often has argued with Coleman about ambulance policies, and occasionally has been left out of department decisions regarding the ambulance service, sources said.

Cavenagh is the ninth city ambulance service director since Barry appointed Coleman acting fire chief in 1982. Three directors were appointed temporarily in 1987 alone -- and soon replaced.

Some officials interviewed said that Cavenagh was "fighting for every inch" with Coleman about suggested improvements to the ambulance service, chief among those giving the District medical community a greater role in shaping and reviewing ambulance service policies.

At a mid-December meeting of the city's emergency medical services advisory committee, Cavenagh said that one of his chief concerns was the lack of medical oversight of the ambulance service, according to the minutes of the meeting. His plans to have medical officials involved may be the source of some friction with Coleman, sources said.

Cavenagh has declined to explain his agenda publicly. He had scheduled a news conference for yesterday morning, but it was postponed until next week. Fire Capt. Theodore Holmes, a department spokesman, said the news conference was postponed on Thursday because ambulance officials were "too busy" this week reviewing complaints of slow ambulance service.

In a telephone interview yesterday, Cavenagh said that he and Coleman "certainly had differences of opinion," but denied that a serious dispute existed. Cavenagh said, however, that two recent Fire Department orders changing ambulance policy were made without his consultation.

Sources also said that in a recent Fire Department meeting Coleman allegedly responded to a remark Cavenagh made by telling him to speak only when asked to speak. In addition, Coleman recently complained when City Administrator Downs and Cavenagh met privately.

Cavenagh declined to confirm those incidents.

Two city task forces, as well as an outside consultant, have studied the city's ambulance service in the past two years. Each has recommended sweeping policy and procedure changes to upgrade the system, but some of those who participated in the task force admitted this week that few, if any, signficant changes have been made.

"I don't know how the Fire Department can continue to abrogate its responsibility to this crisis," Dr. Harry Champion, director of the Washington Hospital Center's trauma unit MedStar, said this week.

Holmes, the Fire Department spokesman, said yesterday that ambulance service problems cannot be solved quickly. "We didn't get where we are now overnight, and we won't get better overnight," he said. The ambulance service is considered to be one of the busiest -- and slowest -- in the country, according to task force reports.

"It's extremely frustrating," said one official. "I guess the right person hasn't died yet because of ambulance mistakes. Until that happens, it appears no action will be taken."