The Federal Trade Commission has rejected an agreement signed by Chrysler Corp. and the FTC's staff that would have resulted in Chrysler paying millions of dollars to consumers for the repair of engine damage in up to 38,000 cars, sources said yesterday. The action is the first time in recent memory that the FTC has turned down an offer by a company to provide redress for consumers.

The agreement was disclosed by informed sources as the FTC issued a separate consent agreement with Chrysler, which requires the troubled automobile manufacturer merely to notify owners of 700,000 Japanese-made cars sold by Chrysler that special oil filters are needed to avoid another kind of engine damage. No money is involved in the deal approved by the FTC and announced yesterday.

Rejection of the other agreement -- which has left key FTC staff members bitter and fearful of the agency's future direction -- came on July 30 after FTC economists suggested that in order for consumers to solve the engine problem, they would have had to switch from leaded to unleaded gasoline. Chrysler could have sent as much as $7 million for the repairs to consumers. In fact, sources said the payments to consumers would have been almost totally paid for by Mitsubishi under a reimbusement agreement with Chrysler.

The decision is viewed by some FTC officials as symbolic of the agency's continuing hesitancy to bring tough cases that would rankle the business community and the Reagan administration. James C. Miller III, an Office of Management and Budget official and staff director of the administration's regulatory reform task force, has been nominated to become chairman of the agency beginning later this month.

Although the rejected agreement was not disclosed because of commission confidentiality rules, former FTC chairman Michael Pertschuk dissented from the oil filter decision because of his concern about the rejected decision.

That decision centers on early failures of balancer chains in up to 38,000 of Chrysler's Dodge Colts and Plymouth Arrows, which are built by Mitsubishi. The chains were developed to reduce engine wear by cutting vibration. The cars were sold during the 1976 and 1977 model years, Pertschuk wrote in a dissent released yesterday with the decision.

"Chrysler failed to tell its customers of this problem after learning about it," Pertschuk wrote. He could not be reached for comment yesterday.

At a meeting on July 29, the FTC was deadlocked on the Chrysler payment plan along party lines, with Democrats Pertschuk and Paul Rand Dixon voting for acceptance of both agreements with Chrysler and acting Chairman David Clanton and member Patricia Bailey voting against. The next day an agreement was worked out to accept only the oil filter portion of the package.

"Though the facts are open to reasonable dispute, I think there is reason to believe that Chrysler had a duty under the FTC act to dislcose the balancer chain problem to its customers," Pertschuk wrote.

But Clanton and Bailey said in a joint statement that Chrysler could not propose cost-effective actions for consumer to solve the problem. "The only use and care information that the company could have communicated to current owners during that time that might have reduced the likelihood of premature balancer chain wear was to advise them to use unleaded gasoline," they wrote.

The two members -- who admitted that the company was "possibly in technical violation" of the FTC act for about four months -- noted that analysis by FTC economists indicates that the higher costs of buying unleaded gasoline would have exceeded the cost of replacing the balancer chain.

The FTC economists said it would not make sense for consumers to spend more for unleaded than leaded gasoline because that amount is greater than the $150 to $250 for a new balancer chain.

Pertschuk disagreed with Clanton and Bailey. "The evidence indicates that consumers could have avoided or deferred substantial economic loss if they had been told about the balancer chain failure in time," he wrote.

While refusing to respond to questions on the agreement signed by Chrysler, Clanton said in an interview that "from the standpoint of what our resources are, and our legal duty must be, we can't expect manufactuers to become absolute guarantors for their cars.

"Even if a company was willing to ante up," that shouldn't determine "what our response should be," Clanton said. "We are not taking the position that any kind of defect is a law violation. Manufacturers are not automatically liable."

In the agreement released yesterday, the FTC said Chrysler provided inaccurate information about oil filters to owners of some 1971-to-1980 Dodge Colts, Colt Hatchbacks, Challengers and D-50 pickup trucks, and Plymouth Arrows, Sapporos and Champs. The company is required to send cards to owners of these vehicles explaining how to avoid oil filter leakage problems.