The key government index designed to forecast changes in the economy rose sharply last month, the government reported yesterday - ending three months of sluggishness that some anaylsts feared might portend a prolonged slowdown.

The Commerce Department announced that its index of leading economic indicators rose a robust 0.8 per cent in August - the steepest jump since March, when the economy was rebounding from the effects of the stifling winter cold spell.

At the same time, the agency revised its July index to show a modest 0.2 per cent rise, rather than the 0.2 per cent decline reported in preliminary estimates, reversing what would have been the third monthly drop in a row.

The combination of figures was heartening to economists, who earlier had worried that the downturn in the index might be pointing to another prolonged doldrums period, such as the one that prevailed in the final few months of the Ford administration.

Treasury Secretary W. Michael Blumenthal termed the August turn-around "encouraging." Blumenthal told a press conference that policy makers took "some degree of a comfort" that "things seem to be picking up."

Although analysts cautioned that a single month's statistics are not always reliable, economists said the August figures suggested that the slowdown may be ending and the recovery may be about to resume a more vigorous pace.

Maynard, S. Comiez, the Commerce Department's deputy chief economist, said current expectations are for the economy to grow at a 3 to 5 per cent annual rate this quarter and then speed up somwewhat during the final three months of the year.

The recovery has been undergoing an adjustment from the rapid, but unsustainable pace of the first and second quarters to what analysts predict will be a slower, but still respectable pace during late 1977 and early 1978.

Blumenthal reiterated that the administration still believes "we achieve 5 per cent growth in real terms or something that is very close to it" in 1978. Based on forecasting models, he said, "We have a chance of achieving our" predictions.

However, forecasters still are uncertain about the likely performance in the second half of 1978, when some economists are predicting the recovery will weaken. Several prominent forecasters have predicted the economy may slow to below 4 per cent - the pace needed to keep the unemployment rate from rising.

Blumenthal insisted yesterday he still was optimistic about the longer-run earlier by Charles L. Schultze, President Carter's chief economist, that if the recovery falters, the administration will take new steps to bolster it.

"There is enough time to take action . . . if needed," he told reporters.

Yesterday's report showed favorable trends in six of the ten individual indicators included in the August statistics. Three other components declined, and one - the layoff rate of workers - remained essentially unchanged.

Among those on the rise were change in total liquid assets, change in sensitive prices, contracts and orders for plant and equipment (in 1972 dollars), money balance (in 1972 dollars), new orders for durable goods, and bulding permits.