Unemployment last month remained at 9.5 percent, the highest since World War II, while a number of signs indicated that the job market worsened, the government reported yesterday.

The number of factory jobs fell in June, the unemployment rate among adult men rose to a new record of 8.7 percent and black teen-age unemployment exceeded 50 percent for the first time, reaching 52.6 percent. Additionally, the number of "discouraged workers"--those who want jobs but have given up the search as hopeless--rose 160,000 to a record 1.5 million during the three months ended in June.

The White House yesterday predicted "a few more months of high unemployment," and some economists cautioned that the overall jobless rate may rise a little further in coming months even with the recession now bottoming out. White House spokesman Larry Speakes said President Reagan "is particularly sympathetic and concerned with the plight of the unemployed but we believe that it's important that we now go ahead" with Reagan's economic program.

The jobless rate for all blacks declined slightly to 18.5 percent in June, but was still more than double the 8.4 percent rate for all whites.

Unemployment often stays high after the end of a recession, and will only start to come down when the economy begins to grow strongly. Many analysts, including some Reagan officials, fear that recovery from the present recession will be only sluggish, especially if there is no relief from present high interest rates.

There has been "no real signal that the economy is about to take off," the Commerce undersecretary-designate for economic affairs, Robert G. Dederick, commented yesterday, adding that it is "still bumping along the bottom." There is "nothing in the data for June to indicate anything resembling a turn" in the economy, said Alan Greenspan, one of the outside economists who advise Reagan. However, he agreed that the economy is now "close to, if not at" the bottom of the cycle.

The major problem, Greenspan said, is that "while signs of recession are over, or close to over, the signs of an actual upturn are lacking."

Bureau of Labor Statistics Commissioner Janet Norwood commented that there were especially large job declines in machinery and textiles, but "small reductions occurred in almost all of the individual manufacturing industries."

Industrial jobs fell in total by 140,000 during June to 90 million. The bulk of the job losses came in manufacturing, with a slight rise in the number of service jobs, after seasonal adjustment.

Changing seasonal factors may have distorted the June employment data, analysts said yesterday, with fewer students and school-leavers entering the labor force than usual for that month.

Normally in June there is a big influx of students into the labor force and a jump in both employment and unemployment. "It is possible that, since the June survey week was early, some of those who usually enter the labor force in June will not be reported until July," Norwood said. This would have the effect of raising the seasonally adjusted figures for the labor force and probably for unemployment later this summer.

June's raw, unadjusted employment figures showed the jobless rate increased sharply from 9.1 percent in May to 9.8 percent, with a total of 10.9 million people out of work compared with the 10.4 million shown after seasonal adjustment.

Earlier this year Reagan criticized the press for writing only about the adjusted unemployment numbers, which at that time looked worse than the raw figures. He said, "I'm not sure we live in a seasonally adjusted world."

One clear improvement in yesterday's report was a decline of 320,000 in the number of people forced to work part time because of a lack of full-time jobs. "This was the first substantial decline in some time for this group, which is often called the partially unemployed," Norwood said.

High unemployment has held down wage increases. The government's index of hourly earnings rose by only 0.2 percent in June, to a level 6.9 percent above a year earlier. This compares with a rise of 8.9 percent in the previous 12 months.

The Federal Reserve yesterday reported a sharp decline of $2.2 billion in the key M1 measure of the money supply, which includes currency and checking accounts, in the week ending June 23. The previous week's level was also revised downward by $300 million.