Union leadership checks the jobless numbers and finds little to cheer

America's unemployment rate showed continued improvement in June. But labor economists are not convinced that the figures are as encouraging as the Reagan administration says they are.

The nation's jobless rate dropped for the fourth straight month to 10 percent , the lowest since last August. This is a decline from 10.1 percent in May, resulting from major gains in manufacturing employment.

President Reagan said he was ''heartened'' by the latest unemployment figures. He conceded that ''we still have a long way to go,'' but said, ''Day by day, month by month, America is gaining strength and moving forward. . . . The recovery is spreading.''

Treasury Secretary Donald T. Regan, also encouraged by the latest report, said it indicates that ''right now we are in the beginning of an upward phase'' in rehiring. If it continues, he said, ''by the end of the year I think we'll see unemployment down . . . in the 9 percent area, and next year we'll see it in the 8 percent area.''

The AFL-CIO finds less encouragement in the June figures released last week, although Rudy Oswald, the federation's research director, describes the employment figure as ''a welcome sign.'' He said there is little basis for optimism in figures that show unemployment of 11.1 million virtually unchanged from May, one-fourth of those on the rolls out of work for six months or longer, the duration of unemployment continuing to lengthen month by month, and only half of those now unemployed receiving jobless benefits.

''The recovery is not yet strong enough to generate any meaningful recall of laid-off workers,'' Mr. Oswald said. ''If jobs are not available, the recession is not over.''

AFL-CIO economist John Gillespie added that ''the modest recovery so far has not reduced massive unemployment significantly.''

He also said there has been no real improvement in the ''execessively high'' number of workers who have given up looking for work because they do not believe jobs can be found.

The June Labor Department report said there were 1.7 million ''discouraged workers'' who are jobless but not seeking employment.

Democratic presidential hopefuls who see high unemployment as a major political issue have been echoing the union position, but the AFL-CIO does not limit its criticism to the Reagan administration and its economic policies.

The federation complains that Congress must share the blame because it ''has only scratched the surface of the kind of job creation needed. . . . The jobs program passed this year is simply not enough.''

It is calling on Congress to make its top priority ''writing bigger programs to create jobs in housing and public works'' to restore jobs lost in the depth of the recession.

Administration analysts report ''strong employment growth'' in June and note that the number of people holding jobs (100.8 million civilians and just under 1 .7 million in the armed forces) shows a gain of more than 1 million during the past six months. Except for sharp increases in the labor force, the Labor Department says unemployment would now be under 10 percent.

Among encouraging signs of an upturn in manufacturing, auto unemployment has dropped from 22.3 percent to 13.3 percent since Jan. 1, and the jobless rate in steel and other metals industries has dropped from 28.6 percent to 19.4 percent.

June figures showed a 9 percent unemployment rate for adult men (down 0.6 percent), 8.6 percent for adult women, 8.6 percent for whites, 20.6 percent for blacks, 14 percent for Hispanics, 23.6 percent for teen-agers, and 50.6 percent for black teen-agers (up 2.4 percent).