President Reagan announced last night that his administration is revising its economic growth forecast for this year substantially upward, and aides said they now expect unemployment to be down to about 9.5 percent by year's end. It is 10.1 percent now.

The higher growth forecast, if it comes true, would also mean a $10 billion to $15 billion lower federal deficit in fiscal 1984, which begins Oct. 1.

But aides said they did not expect the more rapid recovery to translate into higher inflation than previously forecast.

Thus their new predictions, which are distinctly more optimistic than those of most private forecasters, contain all good news and no bad.

Reagan disclosed the new forecast in his opening statement at last night's news conference.

He used it to buttress his arguments against capping the third year of the tax cut he pushed through Congress in 1981. That third installment, which will be accompanied by a 10 percent reduction in withholding rates, is scheduled to take effect this weekend.

House Democrats voted last week in the name of fairness and reducing the deficit to cap the forthcoming cut so no household would gain more than $720. This cap, which would be felt mostly by households with incomes over $50,000 a year, will be voted on today in the Senate.

"America's economy is beginning to sparkle," Reagan said last night. He repeated his threat to veto any reduction in the tax cut. In a jab at the Democrats, he said "their tax cap must not and will not become law because fairness is not slapping tax increases on 2.4 million small businesses, 350,000 family farms and millions of middle-income married couples who filed joint returns. Fairness is not appealing to envy, pitting group against group . . . . True fairness means honoring our word."

The new forecast envisions a 5.5 percent increase in economic output from the fourth quarter of last year to the fourth quarter of this. That is up from 4.7 percent forecast in April and 3.1 percent projected in January.

Martin S. Feldstein, chairman of the Council of Economic Advisers, said last night that the administration also has revised upward its forecast for 1984 growth from 4 percent to 4.5 percent.

Feldstein acknowledged that the new estimates are "a little higher" than most private forecasts, which is a shift toward optimism, since the original administration growth estimate for this year was lower than most others. The administration had said earlier that a slower recovery was necessary to keep containing inflation; the new forecast implies that it is not.

Feldstein said the new forecast was in part a reflection and extrapolation from the higher-than-expected growth recorded in this second quarter of the year. Growth in the first quarter was a fairly weak 2.6 percent annual rate, but preliminary Commerce Department estimates for this quarter are 6.6 percent.

The new forecast implies rates of well over 6 percent for both the remaining quarters of this year as well. This would drive unemployment down from the 10.1 percent in May to about 9.5 percent, the administration estimates. It would reduce next year's projected deficit from around $190 billion to $180 billion or less. The administration has been criticized heavily both for driving up unemployment and for the coming deficits, which many say are so high they could choke off the recovery in the years ahead.

Economist Alan Greenspan, who was chairman of President Ford's council of economic advisers and remains an adviser to this administration, said last night the new forecast "is not outside the realm of reasonableness," but added, "That has got to be in the upper range of all forecasts. It is not the most likely forecast."