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WASHINGTON — The nation’s unemployment rate dropped to 7.1% in June, the Labor Department reported today, despite the strike against AT&T; and more job losses in the oil and gas industries.

The June figure was an improvement over the 7.3% unemployment level recorded in May and returned the level of American joblessness to the number reported in April--also 7.1%.

(California’s unemployment rate for June was reported at 6.5%, down from 6.7% in May.)

The department’s monthly nationwide household survey showed civilian employment totaling 109,673,000, an increase of 563,000 jobs from May. The labor force, people with jobs or looking for

work, grew by 452,000 to 118,116,000.

The big gain in employment benefited a variety of segments of the population, including adult men and women and Latinos, who showed the largest improvement.

But a separate calculation, done from business payrolls, said employment actually fell in June, by 89,000 workers.

Factory employment was down in June--largely because of the strike by 155,000 members of the Communications Workers of America against AT&T.;

The Labor Department said the drop in factory employment last month “was almost all strike related.”

There were significant job losses, however, in the machinery industry as well. “Part of that weakness can be traced to job losses in factories which manufacture oil field machinery,” the

government said.

Following a trend, another 15,000 workers lost their jobs in the oil and gas industries in June, the figures showed. Since employment in those industries peaked in March, 1982, almost

320,000 oil and gas workers have been thrown out of work.

Presidential spokesman Larry Speakes, in a written statement, welcomed the report of an overall decline in unemployment as “more good news for an economy that is still growing, now for the

43rd consecutive month.”

Unemployment among Latinos fell to 10.6% in June, a 0.4 percentage point improvement. For other segments of the population, the department showed these unemployment figures:

While heavy industries continued to show job losses, new gains were posted for service industries, which added 145,000 jobs in June.