In another sign the recession may have hit bottom in July, output from the nation's factories rose 0.5 percent in August following six consecutive monthly declines, the Federal Reserve Board reported yesterday.

The gains in industrial production were widespread, with particularly large increases in the output of construction supplies and consumer goods such as appliances and furniture, the board said.

The board also revised its estimate of the July drop from 1.6 percent to only 1.1 percent. With that change, the index of industrial production now is estimated to have fallen 8.5 percent from January to July and still remains well below its earlier peak.

Production of construction supplies jumped 2.4 percent in August, reflecting in large part big increases in the number of new houses under construction since May. However, some analysts are concerned that the recent rise in home mortgage interest rates, which are approaching 14 percent in many parts of the country, once again could choke off the housing market. Should that happen, the analysts warn, the number of new housing starts could tumble again.

A further large drop in automobile assemblies last month -- production lines were running at only a 5.6-million-unit annual rate, down 12 percent from July -- was almost large enough to offset the improvement in production of consumer home goods. Part of the reduction in auto assemblies was a result of shortages of parts for some models, the board said.

The output of basic materials, such as steel and cement, rose 1 percent in August. Production of metals rose, as did that of parts for consumer durable goods. Energy production was about unchanged.

The production of business equipment fell 0.5 percent as many firms continued to trim their investment plans modestly. Spending by business has held up well enough during the recession, however, that production of this equipment has fallen only 2.5 percent since August 1979, much less than the 7.6 percent drop in the overall production index.

Consumer spending began to rebound in June, according to retail sales figures.