The controversial Firestone 500 steel-belted radial automobile tire has a "safety-related defect" that has led to thousands of failures and subsequent deaths and injuries, according to the Department of Transportation. The agency yesterday proposed a recall of all Firestone 500s still on the road.

The action could cost the Firestone Tire and Rubber Co. hundreds of millions of dollars since, under federal regulations, every tire sold within the past three years would have to be replaced by the company free of charge. Tires sold more than three years ago would be replaced with the owner paying a pro rate replacement fee.

Under its bylaws, the National Highway Traffic Safety Administration, which issued yesterday's "initial determination," will give Firestone and others an opportunity to respond to its finding at a public hearing Aug. 7. After that the agency can issue a "final determination" ordering the recall.

Firestone said more than 13 million of the tires are still on the road, 2 million fewer than the company estimated to the government several months ago. The proposed recall would also involve tires manufactured by Firestone for Montgomery Ward (known as the Grappler Radial 8000 series) and Shell Oil Co. dealers (the Super Shell Steel Radial).

The tire in question was phased out of production, beginning in early 1977. But Firestone has acknowledged that it was still making some as late as early this year.

Firestone said through a spokesman in Akron, Ohio, that "we do not believe the proposed recall is justified. There is no safety-related reason for the public to be concerned about continuing to use the Firestone steel-belted 500 or any other Firestone-made tire."

Firestone director of public relations Bernard Frazier stressed that the DOT announcement "does not mean that a recall is now taking place or will take place."

He said the company expects to "respond to the NHTSA with our reasons why the recall is not necessary," and added that the agency cannot act until "additional prescribed procedures are followed."

Clarence Ditlow of the Center for Auto Safety, a Ralph Nader group, called on Firestone to recall the tires immediately.

Nader issued a statement urging owners of the tires to go to their dealers and demand replacements. If these are not provided. Nader said, owners should take Firestone to Small Claims Court.

NHTSA head Joan Claybroook said that her agency's action resulted from an investigation that began last February "because of more than 500 reports from consumers who told us about blowouts, blisters, cracks and tread separations."

That investigation, she said, eventually looked into almost 7,000 consumer complaints dealing with "more than 14000 individual tire failures. 29 deaths, more than 50 injuries and hundreds of property-damage accidents."

Many of the complaints came to NHTSA from the Center for Auto Safety, a Nader group, and other consumer groups and members of Congress.

In addition. Claybrook noted. Firestone's "adjustment rate" - the number of tires it has had to replace due to consumer complaints - was found to be significantly higher than the adjustment rates of five other tire manufacturers checked. "In fact," she said, "Firestone's rate was two times greater than any other tire."

Firestone has indicated that it has had to adjust more than 1.5 million of the tires. NHTSA said.

NHTSA has asked a federal court here to force Firestone to answer questions about the tires. Firestone has resisted calling the request "so vague and sweeping that it is not relevant to this inquiry." "The number of questions they have asked would require 100,000 man-hours to comply with," spokesman Frazier said yesterday.

He also said Firestone has provided some 16,000 documents to NHTSA and to a House subcommittee headed by John E. Moss (D-Calif.) that has held hearings on the Firestone 500 situation. Another of Moss' panel's hearings is scheduled for tomorrow.

In 1974 NHTSA recalled 400,000 Firestone 500 stell-belted radials that had been made in late 1973 at the Company's Decatur, Ill., plant, citing safety-related problems. And in 1975 an attempt by the agency to recall ply tires was thwarted when the company took NHTSA to court and the agency backed off.