The U.S. Postal Service received permission yesterday to increase class postage from 15 cent to 18 cents and the cost of mailing a postcard from 10 to 12 cents.

The new rates, recommended by the Postal Rate Commission would mark the fifth increase since 1970, could take effect as early as mid-March and would result in higher parcel post costs and possibly higher prices for some magazines.

Because the rate commission recommended increases lower than those sought by the Postal Service, additional increases probably will be needed sooner than postal officials had estimated, perhaps in two years, commission chairman A. Lee Fritschler said.

The Postal Service governors, who have the final decision on rates, are expected to take up the issue March 3 and usually approve the rate commission's recommendations, Postal Service officials said.

Three years ago, the cost of a first-class stamp was increased from 13 cents to 15 cents, and the Postal Service recently had sought a 20-cent stamp and a 13-cent postcard. The rate commission's decision was the second defeat within 12 hours for the financially troubled Postal Service.

On Wednesday, President Reagan proposed a $632 million reduction in its federal subsidies for fiscal 1982 Fritschler told a Senate subcommittee yesterday that if the cuts are made, nonprofit mailers now receiving discount rates may be forced to pay regular rates and that Saturday mail delivery, rural deliveries or other services could be curtailed.

Fritschler also said the commission is considering initiation of a rate case to examine allowing customers who do not require speedy service to pay a lower first-class rate and receive slower service.

Postmaster General William F. Bolger warned the rate commission in a speech before the National Press Club earlier this month not to reject his request for a 20-cent stamp and other increases. He cited the effects of inflation on postal costs and the proposed subsidy cuts facing the agency.

Bolger said then that he would not eliminate Saturday mail delivery and would seek productivity gains and other measures instead. He had no comment on yesterday's decision by the rate commission.

Fritschler called the decision anti-inflationary and said it would generate enough funds for the Postal Service to operate for at least the next two years. The timing of future increases will depend on inflation, expenses, productivity and mail volume, he said. Bolger had said he hoped that the next rate increase would not be needed for another three years.

The Postal Service had requested a $3.75 billion increase in rates, but the commission approved $2.7 billion because some figures used by the agency to support its request were incorrect, Fritschler said. For every penny increase in first-class rates, the Postal Service receives $600 million, he said.

The rate commission recommended:

Increasing mailing costs for time-sensitive periodicals such as Time and Newsweek by 2.4 cents per magazine.

Increasing parcel post costs 13 percent, which is 2 percent more than requested by the Postal Service.

Raising the cost of third-class advertising mail from 6 to 24 percent, depending on whether it has been presorted by the mailer.

Providing a discount for parcels sent and delivered within the area served by a bulk mail center. The Washington-area bulk mail center serves mailers from Richmond to Baltimore.

Allowing a 50-cent surcharge on heavy or bulky postages that cannot be handled by the Postal Service's mechanized equipment.

Expanding discounts to business mailers who presort.

Increasing first-class letter rates from 13 to 17 cents for each additional ounce.

The postal governors can accept the recommendation or return them to the rate commission for reconsideration. They also can approve the rates under protest, allowing the higher rates to take effect while officials seek to overturn the recommendations in court.