A surge in demand for emergency ambulance service in the Distirct of Columbia has forced Mayor Marion Barry to dip into the city's scarce financial resources to buy three new ambulances and pay the crews to operate them. The projected cost is $948,000.

Fire Department ambulance crews, which provide almost all the emergency sickness and accident transportation in the city, are answering an average of 259 calls a day. That is said by the city budget office to be the heaviest ambulance workload of any emergency service in the country, and the average response time of 8.6 minutes is considered "an unacceptable risk to the lives and well-being" of city residents, according to the Fire Department.

The amended city budget for 1982, which Barry submitted to the City Council last week, provides for the expenditure of $395,000 to buy three emergency vehicles, which would bring the fleet to 17. The rest of the money would be used for additional gasoline, for parts and equipment, and for the salaries of 36 additional "emergency medical technicians."

The addition of three ambulances, the mayor said, will enable the fire department to cut the average response time to five minutes, which it regards as adequate.

Statistics provided to the City Council with the budget request show a dramatic increase in demand for ambulance service by city residents during the past 14 years. In 1967, when the District's population was about 860,000 fire department ambulance crews handled 46,696 calls. Since then, the population has dropped to about 638,000, but this year the department expects 94,700 calls.

Most of the increased demand is caused not by residents but by the growing number of commuters who work in the city and by tourists, according to Fire Battalion Chief Maurice D. Kilby. He said that there are actually about 1.5 million people in the District on an average workday, and "if any of them gets sick or hurt, I don't care where he lives, he calls us. You can't go by the census figures."

In addition, Kilby said, the city's financial problems have caused the closing of neighborhood health clinics and other medical facilities, with the result that "people who get sick have no choice but to call an ambulance."