Sales of domestically produced new cars fell 16.4 percent in the first 10 days of July from the same period a year ago, according to data released today by the five major U.S. car companies.

The daily selling rate of 13,540 cars for the July 1-10 period was the lowest since 1958, when 12,038 were sold each day.

Analysts said that, although the sales of 108,318 cars in the eight selling days of early July were behind the 129,572 sold in the period last year, it was a bit of an improvement over sluggish June sales.

And General Motors Corp., which had an 18.9 percent decline in early July, announced a dealer incentive program on slow-moving subcompact and compact models. That should help spur sales later in the month, analysts said.

GM said it sold 61,844 cars in the July 1-10 period, down from 76,296 in the period in 1981. Ford Motor Co.'s tally was 29,071 cars, down 3.7 percent from 30,182. Chrysler Corp. said it delivered 13,817 cars, down 15.9 percent from 16,435 in the same 1981 period.

Sales for American Motors Corp., which only releases monthly sales figures, was estimated at 2,200, down 38.1 percent from 3,555, and Volkswagen of America Inc. was off 55.3 percent, from 3,104 last year to 1,386.

All the automakers except GM had sales incentives in effect during the period.

Arvid Jouppi, an auto industry analyst at Colin Hochstin Co. in Detroit, said the seasonally adjusted annual rate for July, based on the first 10 days, could be about 4.9 million vehicles. That would be only a marginal improvement from June's poor results.

John Hammond, an analyst at Data Resources Inc. in Lexington, Mass., said Ford's comparatively good showing for the period might result from the fact that the automaker will wind up a promotion later this month.

Traditionally, the final sales periods of a promotion are strong because buyers rush to take advantage of the offer, he said.

Ford is offering extended warranties and free maintenance on some luxury and subcompact models through July 31.

For 1982 so far, the five automakers sold 3.043 million new cars, down 11 1/2 percent from 3.44 million in 1981.

Dealers said that GM's incentive program will give dealers $400 for each of the following models sold through Aug. 31: the Chevrolet Chevette, Cavalier and Citation; Pontiac T1000, J2000 and Phoenix; Oldsmobile Firenza and Omega; Buick Skyhawk and Skylark; and Cadillac Cimarron.

All but the Chevette are front-wheel-drive models introduced by GM in the past two years. Industry trade publications reported earlier this week that GM has backlogs ranging between 77 days and 171 days of the cars. A 60-day inventory is considered idea.

Some GM dealers said the $400 payments from GM can be used as rebates, for advertising or for sheer profit. One Chevrolet dealer said salesmen in larger cities where there is more competition likely will hand the money out as rebates.

Two dealers said they liked the program. "We can't afford to have those cars sitting here on Sept. 23," the start of the new model year, one of them said.

In other auto industry developments:

* United Auto Workers President Douglas Fraser predicted that General Motors Corp. and the Japanese automaker Toyota will jointly build cars in GM's vacant Fremont, Calif., assembly plant.

Speaking at a news conference at the Communications Workers of America convention, Fraser said the site is better suited for the work than another at Southgate, Calif.

* Chrysler reportedly told the UAW that it will close its Detroit trim plant next year unless the United Auto Workers union agrees to one of two survival plans. The Detroit News said that one plan involves a series of concessions and work rule changes to improve productivity, while, under the other, Chrysler would sell the plant to employes for a nominal fee.

* GM's Pontiac and Chevrolet divisions are eliminating high-priced frills on their 1983 base-model J cars in an attempt to boost the sales of the poor-selling autos.

Chevrolet will establish its Cavalier Cadet, a stripped version, as its base model, abandoning the base model carrying the frills, while Pontiac plans to make the J2000 S as its base-model J car for 1983.

The Cadet and J2000 S are priced several hundred dollars below the base model Chevy and Pontiac J cars.