The nation's civilian unemployment rate declined to 7.2 percent in November from 7.4 percent, the sharpest drop since June and a sign to many economists that the recent economic slump will not turn into a recession.

The Labor Department reported that 300,000 new jobs were added to the economy last month and the number of employed Americans climbed to a record 105.9 million. The number of people without jobs declined to 8.2 million from 8.4 million, the department said.

The overall unemployment rate, including members of the armed forces stationed in the United States, declined 0.3 percentage points in November to 7.0 percent.

The unemployment rate, which was 7.5 percent when President Reagan took office, is near the lowest level of his administration. The rate hit 7.1 percent in June, but then jumped back to 7.5 percent in July, and had been relatively unchanged since then.

Reagan told a news conference that "we now have more people employed than at any time in the history of the nation.

"We not only put some of the unemployed back to work . . . but we also have kept pace with the increasing number of people coming into the job market," Reagan said.

White House spokesman Larry Speakes said that the employment figures "should provide a Christmas gift early to many Americans."

Janet L. Norwood, commissioner of the Bureau of Labor Statistics, said that most of the increase in jobs occurred in the services sector, particularly in retail trade, where employment grew by more than 115,000.

Norwood said that the government's data indicate a pickup from the slow economic activity in the early fall. In addition, the labor force grew less than usual in November, economists said.

Many economists expected the November unemployment rate to remain unchanged or rise because of the severe slowdown in economic activity in the past few months. Growth in economic activity slowed from its 7.1 percent pace in the second quarter to 1.9 percent in the third quarter.

Few economists said that the slowdown would lead to a recession. However, many said that such slow growth would lead to a "growth recession," which means that economic activity is so sluggish that the unemployment rate would rise.

Economists said yesterday that the unemployment rate often reacts several months after economic conditions change and thus the rate could still rise in the next few months.

Still another camp believes the economy will rebound after a slight pause because consumers' incomes and confidence are still high, interest rates are falling and the Federal Reserve has loosened its grip somewhat on credit.

Allen Sinai, chief economist for Shearson Lehman/American Express, said that the slowdown in economic growth during the third quarter "means somewhere along the line, in the next few months we'll see some upticks" in the unemployment rate. Sinai said that cutting back on employment is usually one of the last measures a business takes when economic conditions worsen.

The November report indicates the current slump "is not going to turn into an outright recession," Sinai said.

In addition, the index of aggregate weekly hours of production rose last month, suggesting that industrial production also increased in November after being flat in October and declining in September.

Norwood said that two-thirds of the job growth in the past two years has been in the services sector and that manufacturing industries have only recovered about 70 percent of the jobs lost during the 1981-1982 recession.

"The number of factory jobs has grown very little since July of this year," Norwood said.

"The decline in unemployment is somewhat surprising in view of the slowdown in the economy," said Jerry Jasinowski, chief economist for the National Association of Manufacturers. Jasinowski said the stagnation of the manufacturing sector and growth in services jobs is "creating a serious imbalance in employment trends."

In addition to the number of unemployed, the Full Employment Action Council said, 1.2 million people are too discouraged by the labor market picture to look for work, and 5.4 million people are working part-time because full-time work is unavailable.

Last month the unemployment rate for whites declined from 6.4 percent to 6.1 percent, and for blacks it declined from 15.4 percent to 15.0 percent, the Labor Department said. The Hispanic rate dropped from 10.9 percent to 10.0 percent.

The unemployment rate for men was unchanged at 6.3 percent and that for women declined from 6.9 percent to 6.6 percent. The teenage unemployment rate declined from 18.8 percent to 17.5 percent. The rate for black teenagers was virtually unchanged at 40.8 percent.

The number of new jobs created according to a separate survey of businesses also showed a 300,000 increase.

The average workweek of production or nonsupervisory workers on private nonagricultural payrolls rose 0.1 hour in November, as did overtime. The average workweek was 35.2 hours and that for manufacturing was 40.5 hours, about the same rates they have been for the past several months.