Led by an upsurge in births to women over 30, the number of babies born to whites in Washington rose by 15 percent in 1981--the most substantial increase here in a single year since the late 1940s, according to a city government report.

Among black residents, births to women in their 30s rose very slightly, the city reported, but births to younger women fell. The total number of black children born in the city continued to drop, declining by 1.7 percent from 1980.

The increase in births to women over 30, particularly those with college education having their first child, is part of a nationwide turnabout in childbearing patterns which has taken place since 1975.

Nationally, the number of births to these "older mothers" rose by 38 percent in the last half of the 1970s, according to the National Center for Health Statistics. This compares to just a 10 percent rise in births to all other women from the low point of the baby bust in 1975.

"Many of these are the women who put off having children while they started their careers," said Iris Kern, a professor of social welfare at the University of the District of Columbia, who has published an extensive study of the oldest group of mothers, those over age 35.

"They know the clock is running out," Kern continued. "If they want to have children, they have to do it now. And when they have the children, the results for most of them are amazingly positive. These are women who are doing what they want to do."

Overall, 7,749 black D.C. residents and 1,583 whites had babies in 1981. The white total was up by 210 from a year earlier, while the black total was down by 135.

Children born to women over age 30 accounted for 53.5 percent of white births in the District in 1981 and about 17 percent of births to blacks.

Since 1975 the number of births to D.C. whites over 30 soared by 67 percent, while those to blacks in that age group climbed by 23 percent, making a 40 percent rise for the city as a whole. From 1980 to 1981 births to women over 30 rose by 18 percent among whites and by a fraction of a percent among blacks.

The figures were compiled by the research and statistics division of the D.C. Department of Human Services.

New data for 1981 from the department also shows that:

* Births to D.C. teen-agers rose slightly in 1981 after declining substantially for more than a decade.

* Abortions by Washington residents fell by 795 or almost 6 percent, compared to a year earlier. But the total abortions of 13,014 still exceeded the number of births by 39.5 percent.

* Some 58.8 percent of children born to city residents were out-of-wedlock, a slight increase that continues a long-term trend. Among blacks there were 5,175 births to unmarried women, slightly more than double the 2,574 births to married women.

The proportion of D.C. births of black children that are out-of-wedlock, 66.8 percent, was higher than the most recent nationwide figure for blacks--55.3 percent in 1980--but it is lower than the proportion in several other big cities, including Baltimore and Chicago. Among D.C. whites, 19.5 percent of births were out-of-wedlock. In 1981, births to married white D.C. women rose by 136, to 1,275, and those to unmarried women by 74, to 308. Nationally, 11 percent of white births are out-of-wedlock.

Infant deaths dropped 7.5 percent to 211 for a rate of 22.6 deaths among children under 1 year old for each 1,000 births.

The death rate for black infants--25.3 per 1,000-- was 2 1/2 times the 9.5 per 1,000 rate among whites. But rates for both races have dropped substantially since 1977, when the city government and local medical groups began a major effort to reduce infant deaths.

Nationally, the infant death rate in 1981 was 11.9 per 1,000.

Warren Morse, the statistician in charge of compiling the new report, said the drop in D.C. infant mortality reflects the success of birth control programs aimed at teen-agers, whose babies account for many of the infant deaths, and of programs providing good pre-natal care to pregnant teenagers.

"I think we've accomplished something here," Morse said. "But we still have to do more."

Explaining the increase in births to older women, Kern said improvements in contraception and legalized abortions have made it easier for women to postpone having children while they establish themselves in professional careers.

The upsurge in divorce, she said, has led to more women having "second families"--after a long interval--as part of a second marriage. Also, improvements in medical care have made late child-bearing safer.

Kern, 43, has a 17-month-old son of her own. "He's marvelous," she said.