President Carter has endorsed a controversial bill that would require the nation to convert to "no-fault" automobile insurance, the bill's principal sponsor said yesterday.

Sixteen states have some form of no-fault, a procedure under which insurance companies automatically compensate auto accident victims without regard to who - if anyone - was responsible for the accident. No-fault thus avoids the costly litigation that follows many accidents.

Senate Commerce Committee Chairman Warren G. Magnuson (D-Wash.) said Carter told him yesterday at a breakfast with members of Congress that he favors the Magnuson no-fault bill and has authorized Secretary of Transportation Brock Adams to give it his general endorsement at a Commerce Committee hearing today.

It is the first time Carter has come out for a national no-fault bill, and Magnuson said the administration backing will help push the bill through Congress after years of narrow defeats.

"This morning he told me he'd authorized Brock to come and testify in favor," Magnuson said.

"I'm very pleased. That's a big help. With that help I think we can win," he added.

Magnuson said he didn't expect Adams to endorse every last comma, but they all favor generally of my bill."

In the past, the bill has been defeated by fierce opposition from some insurance firms (others endorsed it) and the American Trial Lawyers Association, representing lawyers who try auto accident personal injury cases. In 1972 the Senate killed it, 49 to 46. In 1974 the senate passed it 53 to 42 but there wasn't any House action before Congress adjourned. On March 31, 1976, it was killed by the Senate again, 49 to 45.

The bill would set minimum federal standards for no-fault systems in personal injuries involving auto accidents. The states would have three years to set up programs meeting the Federal standards: after that, the U.S. government could move in and set up a program.

Under the no-fault system, auto owners buy insurance covering their own financial losses and medical costs arising from auto accidents. Then, regardless of who is at fault, they are paid for these basic losses without having to sue the other party to the accident. Under the Magnuson bill, no-fault policies would have to reimburse the purchaser for the first $100,000 of his or her own medical and rehabilitation costs, up to $12,000 in lost wages, and for the costs of obtaining a housekeeper or other home-aid care.

The general concept is the same as under workmen's compensation or auto collision insurance, in which car owners buy a policy under which their own insurors pay for car repairs.

The Magnuson bill would allow the injured party in a two-car accident to sue the other for personal damages, but only where losses exceed the amounts paid under no-fault and only where there was severe personal injury, disfigurement or long-term disability.

Magnuson and other supporters contend that by eliminating the cost of litigation, the no-fault system provides larger benefits for the same insurance premiums. According to supporters of the bill, 20 cents out of every premium dollar goes for legal fees and the accident victim gets only 44 cents. Magnuson claims the victim's share would go up to 60 or 70 cents under no-fault.

Consumer and labor groups are supporting the bill. The last two Presidents said they supported the no-fault concept but opposed the federal standards bill, preferring to let the states act on their own without federal pressure. Their spokesmen actively worked against past bills. However, Carter has endorsed the federal standards approach embodied in Magnuson's bill, thus throwing White House support to the measure for the first time.

Carter has hinted at support for no-fault but it wasn't until two days ago, according to executive branch sources, that he "signed off" and gave adams a final go-ahead on the bill.

An Adams spokesman at the Transportation Department would say only that Adams will outline his views today.