The nation's civilian unemployment rate remained steady at 7.1 percent last month, as women continued to fill most of the new jobs created by the American economy.

While the service industries, where women hold a large share of the jobs, continued to outpace other businesses in new employment last month, the number of Americans working in the import-battered manufacturing sector also increased for only the second time this year, the Labor Department reported yesterday.

The Reagan administration hailed the employment figures, which showed an increase of 325,000 Americans working, as a sign that the recovery was continuing on target. The population of employed workers now totals a record 107.9 million.

The increase in employment helped ease apprehensions that the record trade deficits reported Thursday would stunt economic growth for the rest of the year and into 1986.

"The rise in employment is a clear signal that rapid expansion is under way, adding yet another indicator of substantial, sustainable growth in the fourth quarter," said White House spokesman Larry Speakes.

"It looks like the fourth quarter is off to a good start," said Robert Ortner, chief economist for the Commerce Department. He added that the large increase in the number of Americans holding jobs last month "was above average for this recovery period."

Administration economists also were encouraged by the surprising increase of 60,000 workers in the manufacturing sector, which has suffered from heavy job losses as low-cost foreign goods have surged into the country in record numbers. Since January, 270,000 manufacturing jobs have been lost, and the 60,000 gain in October failed to match the decline in September. Employment in manufacturing totaled just 19.3 million last month, 1.8 million below the employment peak there in June, 1979.

"Employment levels in some manufacturing industries are now quite low, and the usual seasonal layoffs may therefore have been moderated," said Janet L. Norwood, commissioner of the Bureau of Labor Statistics, which compiles the employment report.

The biggest increase in jobs last month came once again in the fast-growing service sector, which added 324,000 workers and now employs 73.5 million Americans. The Labor Department recorded continued growth in health care and business areas such as temporary data processing, advertising, computer work and research. Women fill about half of those jobs, as well as large proportions of others in the service sector where there were gains last month, such as managerial and administrative support.

Women now hold 51.4 percent of U.S. jobs, a record that reflects the importance of services in the economy. During the past year, moreover, women have captured two-thirds of the 2.1 million new jobs that were generated by the economy.

"Large numbers of adult women have joined or rejoined the labor force since the recovery began three years ago, accounting for nearly 70 percent of the overall labor force growth," Norwood said yesterday.

With their new job gains, women enjoyed the biggest decrease in unemployment last month, dipping to 6.4 percent from the September rate of 6.8 percent.

Ortner said the growth in women working is part of a trend that began after World War II, but stalled in 1980 during the recession.

The current increase in the number of working women has drawn criticism from some Democrats and labor officials, however, as an indication that the Reagan recovery has added low-paying service jobs, many held by women, at the expense of manufacturing employment that often has higher wages.

Labor Department figures bear this out, showing that, on the whole, manufacturing wages are higher than those in the service industry. But the figures also show there are high-paying service jobs, and that wages in the service sector are increasing faster than manufacturing jobs. "It's a mixed bag," said a Labor Department economist.

The October employment figures also showed that the jobless rate among blacks dipped slightly although, at 15 percent, it was more than twice as high as the rate for the entire work force. Black unemployment was 15.3 percent in September.

The teenage unemployment rate surged to 20.1 percent from the September rate of 17.8 percent. Black teenagers had a 39.7 percent jobless rate in October, up from 38.3 percent the month before.

The unemployment rate has remained static at about the 7 percent level for more than a year despite the recovery, as the number of people entering the work force has roughly matched the number of new jobs created.

Last month's 7.1 percent jobless rate, for instance, was the same as the rate in November 1984. The September rate also stood at 7.1 percent, up a bare 0.1 percentage point from August. Earlier in the year, civilian unemployment had risen slightly to 7.3 percent and remained there for six months.

Total unemployment for October, including the military, was slightly lower, 7.0 percent, the same as in September and 0.1 percentage point higher than in August.