Led by increases in Fairfax and Montgomery counties, the population of the Washington area has grown at a much more rapid rate since 1980 than it did during the previous decade, according to a new U.S. Census Bureau report.

The estimates for mid-1983 also show significant growth in Prince George's County, whose population level stagnated during the 1970s, and in Alexandria, where there was a decline.

Meanwhile, the population loss in the District has slowed, but growth in fringe counties, such as Maryland's Frederick and Virginia's Prince William, is down from the explosive rates of the 1970s.

Overall, the pattern of metropolitan area growth has changed substantially, with stability instead of decline at the center, increased growth in the major suburbs, and somewhat slower growth farther out.

Donald E. Starsinic, chief of the state and national estimates branch of the Census Bureau, said the trends in the Washington area since 1980 are similar to those in many other metropolitan areas, particularly in the Northeast.

"It seems to be that the central cities are stabilizing after declines in the 1970s while nonmetropolitan growth is off," Starsinic said. "It may be that we're returning to a more traditional pattern."

The data for the suburban jurisdictions are part of a new Census Bureau report giving estimates for all counties and independent cities in the United States. The estimates are based on several complex formulas using data from income tax returns, auto registrations, birth and death statistics and medicare and immigration records.

The estimate for the District, putting its mid-1983 population at 623,000, was released in February along with those for the 50 states.

The 1983 estimates were issued by the Census Bureau less than four months after those for 1982. Frederick J. Cavanaugh, chief of the branch that prepared them, said they are based on somewhat less complete data and thus should not be compared directly, but he said the new estimates are expected to have an average error of only 1 percent. "That isn't bad at all," he said, "when you figure we're getting the data out so much sooner."

According to the new estimates, Fairfax County had 649,000 people in 1983 -- up 53,200 or 8.9 percent since 1980. Montgomery County's population topped 600,000 for the first time, reaching 603,900 -- a gain of 24,900 or 4.3 percent.

The three-year gain in Prince George's County was less -- 9,300 or 1.4 percent to a total of 674,400. But between 1970 and 1980 the county grew by just 3,352.

"There's been a real pick-up in construction during the past few years," said Philip Taylor, senior planner for the Maryland-National Capital Park and Planning Commission, which tracks population and development in Prince George's. "It's pretty much all single-family homes, detached and condominiums. There are almost no new rental units, but during the sewer moratorium in the 1970s there was almost nothing going up at all."

Taylor said that virtually all the new growth is outside the Capital Beltway, but he said population in older areas inside the Beltway, which fell almost 10 percent during the 1970s, appears to be stabilizing.

The population of the Washington metropolitan area reached 3,369,500 in July 1983, the Census Bureau said, up 118,700 or 3.7 percent since April 1980 when the official census count was made. The growth rate since 1980 comes to 1.1 percent a year, compared to annual growth averaging 0.7 percent between 1970 and 1980, when the area's population grew by 210,517.

The recent increase still is much less than the 3 percent annual growth rates of the 1960s but John McClain, director of metropolitan development for the Metropolitan Washington Council of Governments, noted that it is in line with forecasts COG made two years ago.

McClain said the population growth is probably propelled by the continued increase in jobs, particularly in Montgomery and Fairfax counties. Also, average household size has leveled off after a rapid decline, he said. McClain suggested that growth may be down in the outer suburbs because more affordable town houses are being built closer in.

"Maybe some of the bloom is off having to drive 20 miles to work," added Richard A. Engels, another Census Bureau official. "That's a possibility."

The D.C. estimate shows a decline of 15,300 or 2.4 percent since 1980, but this is less than half the District's rate of population loss during the 1970s.

In Alexandria, according to the new estimates, the population rose by 2,900 to 106,100 between 1980 and 1983 after a loss of 7,710 from 1970 to 1980. The population of Arlington has virtually stabilized, dropping by only 300 in three years to 152,300, following a loss of more than 21,000 in the decade before 1980.

Among the outer suburbs, Prince William has reached 160,500, a 10.9 percent gain over three years, while Frederick has grown to 120,300, a 4.8 percent increase. But these two growth rates are down from the 1970s. The jurisdiction with the fastest growth rate is Virginia's Stafford County, whose 1983 population was 46,800, a 15.7 percent rise over 1980. But even there, the growth rate is down about one-fourth from the 1970s.

Since 1980, according to the new figures, there has been slight growth in Norfolk and Richmond, both of which lost population heavily in the 1970s. The average annual population drop in Baltimore has been cut by two-thirds.