The armed forces are having the hardest time since the draft ended in 1973 in signing up volunteers, defense officials acknowledged yesterday.

They said that Defense Secretary Harold Brown, while still a believer in the all-volunteer force, has just asked the Army for a detailed report on recruiting problems.

Brown's concern stems from new stastics, showing all four services falling short of their recruiting goals for the nine months ended in June, plus gloomy forecasts about future prospects.

The difficulty in meeting quotas in some cases has resulted in such recruiting frauds as supplying volunteers entrance tests in advance of their examinations. The Army has launched a widepsread investigation of such practices.

The statistical evidence that the services are not able to fill their ranks with volunteers is expected to bring fresh calls for a return to the draft. Legislation to do this is now before Congress, but passage is not expected until until after the 1980 elections.

President Carter, leaning on the advice of Defense Secretary Brown, has taken the position that the all-volunteer military is succeeding and that draft registration is not needed at this time.

Brown and other Pentagon civilian leaders are urging the armed forces to work harder to reduce the dropout rate of the men and women they have already signed up.

These are the trends standing out from the Pentagon latest figures on recruiting:

No service got all the recruits it sought in the nine-month period ended in June 1979 -- the longest drought for the recruiters since the draft ended.

The Army experienced the widest and the Air Force the narrowest gap between the number of volunteers sought and the number signed up in the latest quarter, April through June.

The Army, Navy, Air Force and Marine Corps attained, overall, 91 percent of the Pentagon's recruiting goal for the nine months from October 1978, compared to 96 percent one year earlier.

Every service but the Navy had to settle for a smaller percentage of high school graduates among their volunteers in the April-June quarter.

Blacks continued to represent a bigger percentage of the enlisted force, rising from an overall 23 percent in April-June 1978 to 26 percent in the like 1979 period. The Marines experienced the biggest jump -- from 25 percent black in the enlisted ranks to 29 percent.

Pentagon manpower leaders have been warning that recruiting would get tougher in the 1980s as the teen-age population dropped. But they expected the services to do better this summer as young people opted for the military after exploring other careers. The July figures have not lived up to those expectations.

If recruiting continues to lag and the dropout rate among enlisted people doesn't decline sharply, the Pentagon won't meet the total active duty force of 2.05 million men and women President Carter set down as his objective for Sept. 30, the end of the fiscal year.

The actual strength at the end of fiscal 1979 is now expected to be 20,000 to 41,000 under that goal, according to Pentagon estimates.

Judging by past arguments, such shortages will be interpreted be some as insignificant and by others as ominous -- with Reps. Les Aspin (D-Wis.) and Robin L. Beard Jr. (R-Tenn.) representing the poles of that argument.

"When we try to judge the all-volunteer system by looking at recruiting statistics," Aspin maintains, "we're getting a very distorted picture." The military services, he has stressed, have been recruiting between 98 and 99 percent of the people Congress has authorized ever since the draft ended.

"It has become increasingly apparent that the Army simple cannot attract the quality of personnel at all levels that it needs in order to sustain itself as an effective fighting force," Beard counters. "Nearly 50 percent of the male volunteers test mentally in the lower half of the U.S. population, compared to 32 percent in 1974."

Interpretations aside, here are the Pentagon figures on how well the services did in signing up enlisted men and women in the April-June 1979 quarter: