The U.S. Postal Service proposed new rules yesterday to allow private carriers to deliver letters that have to go place in a hurry.

The proposal, published in the Federal Register, marks the farthest the Post Office has gone in relinquishing some of its power as the nation's sole letter carrier.

It was prompted, say postal officials, by a public call for express service and by the service's own recognition that it could not meet the increasing demand for urgent delivery.

Under the proposal, a private carrier would be permitted to deliver letters if the carrier can show "the value or usefulness of the letter would be diminished unless delivered" in a rush.

One way to show this, the Post Office suggests, will be to charge substantially more for delivery - either twice the applicable first class rate or a minimum of $3.

This, said the agency in a statement, "is intended to test whether the shipper looks to a private carrier because he genuinely attaches an importance to prompt delivery, or simply because he desires to reduce shipping costs effectively."

Carriers also will have to meet the following conditions:

Letters that are going within a 50-mile radius must be delivered within 6 hours if mailed before noon, or by 10 a.m. the next day if mailed after noon.

Letters that are traveling more than 50 miles must be delivered by 10 a.m. the next day.

It is not the first time the postal service has offered to lessen its grip on letter delivery rights. Postal officials have let private carriers take mail to data processing centers. They also have exempted letters that accompany cargo shipments. And they have exempted such special kinds of mail as legal documents and banks checks that pass between some institutions.

In 1970, too, during a nationwide postal strike, the postal service dropped its prohibition against private letter carriers.

But in general, postal officials jealously guard their letter-carrying rights, and, in two recent instances, have taken those who have tried to compete to court.

"We're very vulnerable to people undercutting us because they don't have the overhead costs of a national system like we do," Jerry Belenker, a postal service attorney, said in an interview.

In recent months, the agency has tried to speed up its system, promising overnight delivery of letters and packages through an "Express Mail" program. But private express carriers - notably, Emery Air Flight and Federal Express - have competed well in the package market and proven there i large demand for expedited delivery service.

"Thi is probably the broadest exemption we've allowed," said Belenker about the proposed change. "we expect it will be of some injury to us. How much is hard to say."