The Reagan administration predicted yesterday that unemployment will fall more than previously estimated but prices will rise faster than expected this year and through 1992.

In its annual revisions of the official administration economic forecast, the Council of Economic Advisers said the economy will grow by 3.2 percent during 1987, an inflation-adjusted rate that many private economists think is achievable.

This year's growth rate is the same as the administration forecast last January. The economy expanded at a 3.5 percent annual rate during the first six months of this year.

The forecast for growth in subsequent years was lowered by 0.2 percentage point per year, to 3.5 percent in 1988, 3.4 percent in 1989 and, after a gradual decline during the next three years, to 3.1 percent in 1992. If the administration's new forecast proves accurate, the nation will go 10 years without a recession, equaling the postwar record.

The CEA forecast said the unemployment rate would average 6.2 percent this year, lower than the 6.7 percent rate for 1987 that was forecast last January. During the first six months of the year, the unemployment rate fell from 6.6 percent to 6.1 percent. CEA Chairman Beryl W. Sprinkel said yesterday, however, that he was a bit "squeamish" about the June decline, which may have been due in part to seasonal factors. He suggested that the figure for July -- scheduled to be released today -- may register slightly higher unemployment.

The administration also predicted that prices would rise 4.8 percent in 1987, a substantially faster pace than the 3.8 percent rate in the January forecast. Sprinkel said that nearly all of the one-point increase in the estimate was accounted for by two factors: the spring rise in oil prices and the decline in the value of the dollar against foreign currencies, which makes imported goods more expensive here. However, Sprinkel said, the worst of those influences already has been felt. The revised forecast called for inflation as measured by the consumer price index to decline to a 4.4 percent annual rate in 1988 and 4.0 percent in 1989.

Long- and short-term interest rates also will run a bit higher than previously forecast, the CEA said, partly because current rates are higher than expected, and also because higher inflation tends to raise interest rates.

"In my view, the prospects are good for continued growth with low inflation through 1987 and into 1988, so long as we avoid calls for protectionism and a general tax increase that would abandon tax reform," Sprinkel said. Specifically, he said President Reagan would veto legislation raising the minimum wage, sharply increasing federal health benefits or restricting plant closings. Restrictions on plant closings have been proposed in trade legislation, but Sprinkel declined to promise that Reagan would veto any trade bill over that issue alone.

Sprinkel warned that any increase in tax rates for individuals, which were reduced by last year's tax-revision law, would have a negative effect on the economy. Tax increases that do not raise rates, Sprinkel said, would tend to increase government spending rather than reducing the deficit. Reagan has said he will veto any tax increase. Democrats in the House have called for postponing the additional tax-rate cuts scheduled for 1988 to reduce the deficit. The chances for a tax increase this year have become more uncertain recently as House and Senate negotiators have begun rewriting their deficit-reduction targets for the next fiscal year.

The administration revises its official economic forecast at about this time each year, although release of the numbers this year was delayed slightly to incorporate the most recent economic figures, CEA officials said. The economic assumptions in the forecast will be factored into the administration's revised forecasts for federal revenue, expected later this month.

The projections for economic growth in years after 1987 were revised downward, Sprinkel said, in line with the administration's belief that productivity -- output per worker -- will not increase as fast as it has been rising.

Although there is no official projection for productivity, officials said the forecast is consistent with a rise in nonfarm business productivity of about 1.4 percent in 1987 compared to 1986, and about 1.7 percent per year after that.