The D.C. government, moving to enforce its controversial requirement that new city workers live in Washington, has fired 10 employes and given move-or-be-fired ultimatums to seven others who contend they cannot afford to live in the city on $16,000-a-year salaries.

The dismissals and pending dismissals are the first since the new residency law became effective earlier this year and, in the view of union and city personnel officials, forecast continuing problems for the city in its effort to solve a thorny political question.

In Prince George's County yesterday, the County Council rejected a measure that would have made residence in Prince George's a requirement for hiring. Council members criticized the D.C. government for enacting such a law.

Jose Gutierrez, acting director of the D.C. Office of Personnel, said the city already has been forced to grant exemptions from the residency clause to about 100 doctors and registered nurses who work for the Department of Human Services and D.C. General Hospital "because of the special needs of the government in terms of public safety."

Donald MacIntyre, of the American Federation of Government Employees, one of the largest unions of city employes, said, "Even Mayor Barry had problems finding a house he could afford in the District. With high interest rates, high rents, high taxes and a city financial picture that is doubtful, people don't want to move into the city.

"The City Council knows all this, and they know that housing is short, but they want to increase their tax base so much that eventually, they're not going to be able to recruit anyone," he said.

"Down the road, they're going to have to realize they can't have it both ways," MacIntyre said.

For years, city politicians and jobless residents complained that city jobs belonged to city residents, that in order to create a fluid and economically viable city, city funds paid to city workers should stay there.

But because of the hiring freeze imposed by Mayor Marion Barry on March 1, 1979, as part of his move for fiscal austerity, the impact of the city's 11-month-old residency requirement has been delayed in its impact.

The 10 employes fired were from the Office of Personnel, the Department of Employment Services.

The move-in-or-be-fired notices were sent to seven of 31 firefighters hired earlier this year who lived outside Washington. Old employes are not affected by the new law, but new hires have six months to move into the city.

None of the 31 have moved into the city yet, according to fire department records. The seven who have received notices were hired on June 9 and have until early December to become city residents. For others among the 31, the six-month period will expire later.

"The fire department is unique in that they are being allowed to hire, unlike most of the city agencies," said MacIntyre. "They are sort of on the forefront of the residency requirement issue. Things have gone smoothly so far because the requirements haven't been put to the test."

Some city officials, such as City Council-Member Betty Ann Kane (D-At Large), contend that since the law was passed in 1978 and did not become effective until two years later, "People knew what they were getting into if they were hired after that."

"My feeling," Kane said, "is that [the law's] intention is not to make people move in but to hire people who are city residents. There are lots of unemployed people who would qualify for these jobs. We shouldn't have a whole lot of exemptions because of housing problems. We have all these people living here who don't have jobs."

Ken Cox, second vice president of Local 36 of the International Association of Firefighters, said, however, "Not everyone can be a firefighter. It takes a special sort of disposition."

About half the city's present 38,000 regular employes live outside Washington. The police and fire departments have some of the largest proportions. In the fire department, for example, only 217 of 1,300 uniformed firefighters live in the city.

Firefighter Bill Rabbit, 26, one of the seven who has received a notice, said he felt he was being used. "When we took the entrance exam for the department back in February of 1977, the laws said that you had to live within a 25-mile radius of the city."

In April of 1979, Rabbit, who then lived in Bowie, moved his wife and daughter into a new home in Shady Side, Md., in Anne Arundel County, about 25 miles from the District line. A little more than a year later he was hired. Now he has a problem.

"I had been on the waiting list for my job since 1977, and at the time I felt it was probably one of the best jobs I could have, something I always wanted to do. It was kind of a life ambition.

"But financially, I can't afford to move into the District. The city is noted as being the most violent place in the nation. I want my wife to feel safe when I'm working at night.

"I started working with a real estate man and asked him to bring me a printout of houses in the $50,000-$70,000 range. He brought me a list of about 200. Six were in the range I could afford, and they were shells," he said.

Rabbit also said that new members of the department frequently have trouble establishing credit, and that when landlords find out they're on a year's probation, they frequently balk at renting them an apartment. "With the way the city has been laying off people, they just don't trust us," Rabbit said.

If worse comes to worse, he said, he could move his family in with some relatives who live in the District. "I understand the problems the District is having, but being a firefighter is something I've always dreamed of."