For the first time in the history of the industry, a major auto maker has agreed to buy back cars from consumers because of a manufacturing defect.

The decision came in a little-noticed agreement between the National Highway Traffic Safety Administration and Fiat Motors of North America Inc.-an agreement that also saw the government for the first time classify rust as a safety defect.

After feeding all of the complaints about excess automotive corrosion into a computer, NHTSA officials were able to detect an abnormally large number of Fiats with body corrosion that could weaken critical areas and components of the vehicles

"We became worried that critical operating components, like the brake or clutch pedal, could fall through the floorboards," an NHTSA official said.

Under the agreement announced last week, Fiat must buy back the worst cars at a price determined according to a depreciation formula. If the owners of the cars repurchased by Fiat believe they are not receiving a fair price, they can petition NHTSA for a hearing on the matter.

NHTSA Administrator Joan Claybrook called the Fiat agreement especially significant because of the buy-back provision. Historically, U.S. auto makers have resisted government attempts to force them to take back defective cars.

The buy-back affects only cars purchased after Jan. 15, 1971, because of the eight-year statute of limitations of the National Traffic and Motor Vehicle Safety Act.

The problem of automobile rust and corrosion has been the subject of growing interest by the federal government and consumer groups, particularly since it was discovered last year that U.S. auto makers offer significantly stronger antirust warranties in Canada than they do in the United States for the same cars.

NHTSA has contended that corrosion weakens such parts of cars underbodies as the suspension system, steering system and floor pans.

A failure of weakening of these structures, NHTSA says, can result in accidents.

The problem has led the White House and Department of Transportation to call on auto makers to improve domestic rust warranties.

In a letter scheduled to be sent by the White House and DOT today to all majore domestic and foreign auto makers that sell cars in the United States, the government calls the rust problem serious, and says, "We beleive that automobile manufacturers should provide American consumers with the same rust warrantly they give the Canadian customers."

The letter, which was made available to The Washington Post says "We are greatly concerned about [the] disparity in treatment of Canadian and Americna automobile owners." The letter was signed by Esther Peterson of the White House and Transportation Secretary Brock Adams.

The letter points out that Canadian purchasers of automobiles are given a three-year 74,000-mile warrantly against perforations, and a one-year/24,000-mile warrantly against surface corrosion.

"These warranties will be extended in the 1981 model year to five years/124,000 for perforations and 18 months/37,000 for surface corrosion," the letter said. "In addition, all 1978 and later Canadian autos are warranted for six years/148,000 miles against any structural damage from corrosion."

American consumers "receive a far more limited anticorrosion warrantly," the letter says. "Given the serious nature of the problem and the fact that automobiles sold in the United States and Canadian markets are identical, we believe that manufacturers should provide American consumers with the same rust warrantly they give to Canadian consumers."