Births to Washington residents rose slightly last year for the first time since 1970. according to a city government report.

Among teen-agers, whose babies are most likely to have physical problems, births continued to fall substantially, as they have for more than a decade.

Births to women over 30, particularly those in their early 30s, increased significantly, the new figures indicate, apparently because many women who had postponed having children now have decided to have them.

Arthur A. Campbell, deputy director of the Center of Population Research at the National Institutes of Health, said the report shows "that there are fewer young mothers who are likely to be forced out of school and fewer babies exposed to the problems of having a teen-aged mother."

On the other hand, the increase in births to women around 30, Campbell said, is probably desirable.

"You know these are children that women want to have," Campbell said. "They're not the result of accidental pregnancies, and their parents are likely to have the resources to take care of them. It's a good situation.

According to the new city figures, the upturn occurred in about equal proportions among both blacks and whites living in the city. Overall, blacks accounted for 8,515 of the 9,885 children born to District of Columbia residents last year or 86.1 percent of the total. The number of white births was 1,370.

The new city government data also indicates that:

Washington residents had 12,718 legal abortions last year, about 29 percent more than the number of births. The abortion figure was down by 227 from 1976.

Slightly more than half the children born to D.C. residents last year were out-of-wedlock. Births to unmarried women here accounted for 53 percent of all births in 1977, compared to 52.6 percent of births in 1976.

The total number of births to D.C. residents last was up by 250 from 1976 - and increase of 2.6 percent. During the previous six years, births in the city had declined by 35 percent. The drop was steepest from 1970 to 1974.

Throughtout the United States the birth-rate rose slightly last year for the first time since 1970. However, during the first five months of 1978, there has been a slight downturn.

"You can't really predict what's going to happen here next," said Warren W. Morse, a statistician for the D.C. Department of Human Resources, which compiled the figures. "It depends on so many unknowable factors."

From 1975 to 1977, the number of children born to Washington teen-agers dropped from 2.636 to 2.253 - a decrease of 14.5 percent. The decline was about the same for those 17 and under, who are most likely to encounter severe problems, as it was for 18 and 19-year-olds.

Even so, there were 1,053 births last year to D.C. residents under age 18. Included was one birth to a 10-year-old girl, which Morse said was the youngest age for a mother ever recorded in the District of Columbia.

Births to women over age 30 reached 1,855 last year - 15.5 percent more than in 1975. The increase was most substantial - 27 percent among women 30 to 34 having their first child. Morse suggested that many of these probably were working women who earlier had delayed having a child by use of birth control or abortion. In addition, even though Washington's overall population is declining, there has been a significant increase in the 30 to 34-age group, according to city population estimates.

Morse said the decline in births to teen-agers here has been caused partly by the decline in the number of teen-agers and also by the success of efforts promoting sex education and birth control.

"It shows that something's working," Morse said, "but teen-age pregnancies still are a serious problem, and at 17 and under each one is tragedy."

The availability of legal abortions has been another factor in reducing teen-age births, Morse noted. Last year 2,531 D.C. residents under age 20 had abortions, according to the city government, statistics including 203 who were under age 15, and 1,018 aged 15 to 17.

Overall, 29,545 abortions were performed last year in Washington, including those on city residents and on women coming from elsewhere. The total was down 5.9 from a year earlier and 27 percent below the peak of 40,812 in 1973. Virtually all the decrease is accounted for by fewer nonresidents having abortions here now that abortions are widely available in other states.

Except for age, the city government data gives no breakdown on the characteristics of Washington residents having abortions. However, of all women having abortions here, only 21 percent were married, and about one-third had at least one previous abortion. There were 1,883 who had two previous abortions and 567 who had three or more.

Among D.C. residents there were 1,286 abortions per 1,000 births in 1977, compared to an estimated 370 abortions for every 1,000 births nationwide, according to Planned Parenthood.

The proportion of births that were out-of-wedlock here - 53 percent - also was much higher than the most recent nationwide figure, 14.8 percent in 1976.

Among D.C. blacks the proportion of out-of-wedlock births last year was 59.6 per cent; among D.C. whites it was 12.3 percent. Nationwide in 1976, the proportion of out-of-wedlock births was 50.3 percent for blacks and 7.7 percent for whites.