The nation's civilian unemployment rate fell from a seasonally adjusted 10.1 percent to 10 percent last month as a sharp increase in employment was almost entirely offset by a big jump in the size of the labor force, the Labor Department reported yesterday.

With the economic recovery still speeding up, an additional 1.23 million persons found jobs in June, while the number of people either at work or looking for work rose by 1.18 million. Department analysts said an unusually large number of students sought work last month as summer vacations began.

There were still 11.15 million persons counted as unemployed, a reduction of less than 50,000 from the month before. Nearly 3 million of the jobless had been without work from half a year or longer.

President Reagan said he is "heartened" by the decline in the unemployment rate, which dropped to 9.8 percent if people in the armed services are included in the totals. "We still have a long way to go, but the recovery is spreading," Reagan said.

Council of Economic Advisers Chairman Martin S. Feldstein noted that payroll employment rose by 375,000 in June. "This brings the recovery to a new milestone: The number of people on American payrolls has increased more than 1 million since last December," he said. The civilian unemployment rate peaked at 10.8 percent that month.

Feldstein also rejected "any notion" that the recovery may be going too fast. "The current pace of expansion is both natural and welcome at this stage in the recovery," he said in a statement. "Although it is, of course, possible to have growth that is too fast and that causes an increase in the rate of inflation, we are definitely not growing too fast at this time."

The CEA chairman was responding to reports that he and other administration economic advisers favor actions by the Federal Reserve to slow money growth and hence the pace of the recovery in the future, actions that would involve higher interest rates.

White House officials said flatly on Thursday that they do not want to see any increase in interest rates.

In his statement, Feldstein said that the Fed "can pursue a policy aimed at maintaining a sound rate of economic growth without rising inflation." One component of such a policy would be keeping the money supply from "increasing at double-digit rates for a sustained period of time."

What is worrying some private analysts, as well as those in government, is that the rapid money growth is occurring at a time that the economy already is expanding at a strong rate. If the money growth is not slowed now, the economy could really take off later, producing either more inflation or still sharper actions by the Fed to prevent it.

But restraining money growth--which by some measures has been far more rapid this year than either the Federal Reserve or the administration had intended--usually takes an increase in rates, a point Feldstein acknowledged in his statement.

"No one likes to see interest rates rise," the CEA chairman said. "The substantial increase in market interest rates over the past two months has been a source of concern. But although the Fed could temporarily lower some interest rates by explicitly adopting a policy of rapid expansion of the money stock, this would subsequently lead to higher rates of inflation and higher market interest rates."

The Federal Reserve's policymaking group, the Federal Open Market Committee, meets next week to review money growth targets for this year and set tentative ones for 1984. Federal Reserve sources have said that they expect the committee to tighten credit conditions at that time.

In its report, the Labor Department said that the big gainers in June among demographic groups were adult white males, whose unemployment rate fell from 9.6 percent in May to 9 percent. The rate for adult women rose to 8.6 percent from 8.5 percent. The rate for teenagers climbed from 23 percent to 23.6 percent.

Among racial groups, the rate for white workers dropped from 8.9 to 8.6 percent, that for blacks was unchanged at 20.6 percent, and the rate for workers of Hispanic origin increased from 13.8 to 14 percent.

The department also said that the rise in payroll employment boosted the number of hours worked by 0.7 percent in June, an increase that means that industrial production also increased strongly last month. At the same time, the hourly earnings index went up only 0.1 percent for the month and only 4.6 percent in the past 12 months.

Janet L. Norwood, commissioner of labor statistics, told the Joint Economic Committee that the large increase in employment brought the figures based on a survey of households back into line with the data from payrolls, which had shown stronger employment gains during most of this year.

Norwood said the unemployment rate for adult males is now a full percentage point below its December level, while that for adult women is half a point lower.

"No improvement has occurred in the jobless situation of black workers during the period, however," she continued. "Whereas the unemployment rate for white workers has dropped by a full percentage point since December to 8.6 percent , the rate for blacks--at 20.6 percent--has changed very little over the last six months.

"Looking at the black situation in another way, the employment-population ratio for black adult men was more than 11 percentage points lower than for white men, and the ratio for black teenagers was 26.5 points lower than for white teenagers," Norwood explained.