Retail sales rose 0.8 percent in July, following an even stronger June increase, as consumers returned to auto showrooms and department and furniture stores, the government reported yesterday.

The Commerce Department said retail establishments sold $127.6 billion worth of goods in July, an increase of $954 million from the June level, when sales shot up an even faster 1.4 percent.

While half of the July gain and two-thirds of the June increase came from a rebound in auto sales, many analysts said the back-to-back increases were still impressive following several months of lackluster performance.

"Consumers are overcoming their earlier lethargy and are starting to spend again," said Allen Sinai, chief economist of Shearson Lehman Bros. "The notion that the consumer might fizzle out has been dashed by these numbers."

Sinai said the increased consumer spending was being fueled by rebounds in the country's industrial sector, where production and employment have been rising in recent months. He said the drop in the unemployment rate to 6 percent in July, the lowest level in eight years, meant more jobs and higher incomes.

"The economy seems to be in the best shape and showing the best balance than at any time since early 1984," he said.

Other economists, however, said the spending gains were puzzling because income growth still is not keeping up with inflation and consumer debt burdens remain at high levels.

"When you look at the income numbers, you have to wonder what consumers are spending," said Bruce Steinberg, an economist with Merrill Lynch. "Consumer incomes, their savings rate and level of debt are still negative factors."

Michael Evans, head of a Washington consulting firm, said that consumer spending, excluding cars, has been rising at a rate just below the increase in inflation over the past three months, indicating that higher prices were driving up the numbers rather than increased consumption.

But Sandra Shaber, an economist with the Futures Group in Washington, said the July advance was still "a significant upturn that showed good increases across the board."

Sinai said it was appearing more likely that overall economic growth, bolstered by a recovery in consumer spending, will top 3 percent this year, in line with the Reagan administration forecast. He said virtually all parts of the economy, with the exception of home sales, were showing renewed strength.

A separate report by the National Association of Realtors showed that sales of existing homes in the April-June quarter posted a 5.6 percent increase over the same period a year ago. But sales fell in 15 states and the District of Columbia, with the declines attributed in part to the big jump in mortgage rates during the spring.

The 1.4 percent increase in retail sales in June, the biggest gain since February, represented a large upward revision from the government's initial estimate a month ago that sales had risen only 0.4 percent that month.

Auto sales rose 1.9 percent in July following a 4.5 percent June increase, but analysts said these gains only partially offset earlier sluggishness. They said inventories of unsold 1987 models remain high and will mean further production cutbacks in August.

Excluding autos, retail sales rose 0.4 percent in July and 0.5 percent in June, with both gains the highest since a 2.6 percent rise in February. The strength came in both sales of big-ticket items and nondurable goods.

Sales of durable goods, items built to last three or more years, rose 1.4 percent in July while sales of nondurable goods rose 0.4 percent.

Sales at furniture and appliance stores rose 0.7 percent in July, after setbacks in this category in five of the past six months. Analysts said the gains reflected in part higher sales of window air conditioners because of unusually warm weather during the month.

Sales at department stores and other general merchandise stores rose 0.5 percent in July while sales at clothing speciality stores were up 0.8 percent, reflecting continued strong apparel sales.

Sales at gasoline stations were up 1.4 percent, although analysts said much of this increase represented higher prices rather than increased consumption.

The only weakness in July came in sales at grocery stores, which were off 0.5 percent, and at restaurants and bars, which suffered a 0.6 percent drop.

All of the figures have been adjusted to reflect normal seasonal variations