There was mixed economic news for the administration yesterday as Chase Manhattan, the nation's third-largest bank, raised its prime lending rate by one-half point to 20 1/2 percent, but the Bureau of Labor Statistics reported a sharp drop in unemployment in June to 7.3 percent.

However the jobless rate fall was probably a statisticl quirk, BLS analysts said.

The prime rate rise is a blow to administration hopes that the adoption by Congress last week of the president's tough budget cuts would impress financial markets and help lower interest rates.

But the tight money policy being followed by the Federal Reserve Board, supported by the administration, apparently still is holding interest rates up. sMany analysts had expected rates to decline this week amid indications that the economy is slowing and that thre has been a sharp contraction in the money supply.

Chase was followed by First National of Chicago. The 20 1/2 percent is just 1 percentage point below the record prime level reached last December. The cost of funds for banks has been high this week, with the key Fed funds rate trading at 22 percent yesterday.

High interest rates have been a major reason for the slowdown in the economy, which still is thought to be going on despite the three-10ths of a percentage point drop in the jobless rate last month, back to its level of February to April. The June fall was not a "believable trend," BLS analyst Jack Bregger said.

The White House also immediately cautioned against overoptimism about the unemployment report, and spokeman David Gergen said that the administration does not plan any changes in its economic program as a result of the news.

Treasury Secretary Donald T. Regan said Wednesday that the economy was slowing down and may even decline in the next three months. The president's tax plan, now before Congress, is designed to stimulate growth.

Recent indicators have suggested that the economy now is turning down after very rapid growth in the early months of the year. Regan said he expects unemployment to go up slightly in the coming months. Figures released earlier this week showed the government's index of leading indicators, which give a guide to the future course of the economy, dropped sharply in Amy.

Although unemployment was down last month, there was also a very sharp drop in the number of people in work. The fall of 840,000 in total employment was larger than during the sharp recessions last year and in the middle of the 1970s. Bregger commented that "840,000 is icredibly large . . . essentially a correction for increases in earlier months."

The fall in those employed coincided with a 1.2 million drop, after seasonal adjustment, in the size of the civilian labor force. But this decline was partly because of an earlier-than-usual end to the school year, which upset the seasonal adjustment calculation.

Usually many college and school leavers enter the labor force in June, but this year some colleges finished in May. By the time the June data were compiled, many school leavers had found jobs, and so the seasonal adjustment overcompensated for the influx of young people onto the register.

From a longer perspective, Norwood said, the jobless figures for the first half of the year show "a reasonably stable unemployment situation coupled with some growth in employment," with continuing weakness in payroll jobs in manufacturing and construction.

The settlement of the miners strike led to a jump of 150,000 in mining jobs, but other declines offset this so that total payroll employment outside manufacturing was unchanged at 91.5 million in June. Construction employment dropped by 60,000 in the month, manufacturing jobs were unchanged, and employment in state and local government fell, the BLS reported.

Other reported changes were that unemployment:

Among adult men declined from 6.3 percent to 6.1 percent of the work force,

Among adult women dropped from 6.8 percent to 6.5 percent,

Among teenagers dropped by 0.5 percent to 19 percent,

Among white workers fell from 6.8 percent to 6.4 percent,

Among black workers rose from 14.8 percent to 15.5 percent,

Among hispanic workers was unchanged at 10.2 percent.

Othe figures released by the BLS showed that hourly earnings during June were up by 0.7 percent on average, after seasonal adjustment. Average weekly earnings climbed by 0.4 percent from May. These increases were probably barely enough to keep pace with inflation.

The hourly earnings index, which is adjusted for the effects of overtime and job shifts between industries, was also up by 0.4 percent in June. It was 8.9 percent higher than a year earlier. After allowing for inflation, the index was 0.4 percent down in May from 12 months earlier.