The Board of Governors of the U.S. Postal Service voted under protest yesterday to temporarily allow the price of a first class stamp to rise from 15 cents to 18 cents, but the board said it would immediately seek a permanent increase to 20 cents.

The governors said they wanted the Postal Rate Commission, the independent body that proposed postal rates, to reconsider its recommendation last month for the 18-cent stamp along with other increases They said additional rate increases were needed if the Postal Service is to break even this year and prevent future rate increases.

By accepting the recommendations under protest, the Postal Service can begin receiving the added revenues while applying for the larger increase. The temporary rates will become effective March 22.

"The governors are well aware our decision will not be a particularly popular one," board chairman Robert L. Hardesty said during a press briefing in which reporters were barred from asking questions. "But the governors are responsible under the law for maintaining the financial integrity of the U.S. Postal Service and it sometimes calls for tough decisions . . . I hope the American public will bear with us."

In addition to the 18-cent stamp, the Postal Rate Commission had recommended an increase in the cost of mailing postcards from 10 cents to 12 cents and mailing rates for other classes somewhat lower than those recommended by Postmaster General William F. Bolger. Bolger had sought a 20-cent stamp and a 13-cent postcart. Bolger had warned after the rate commission recommended lower rates last month that if the board of governors he would ask for another rate hike later this year.

"We return this recommended decision to forestall the need to begin another rate case right away," Hardesty said. "The 18-cent stamp is a recommendation for fiscal irresponsibility in postal matters. It is a recommendation for constant rate changing, and it is a recommendation for higher-than-necessary postal rates in the furture."

Hardesty noted that it was the first time the governors ever protested a rate commission decision. But he added, "The present recommended decision is quite a different matter."

Meanwhile, the Reagan administration said yesterday in its latest budget revisions that the postal service's public service subsidy, which supports services such as Saturday mail delivery, will be reduced by $300 million in fiscal 1982. It also proposes a $300 million reduction in the 1982 revenue subsidy that provides free and reduced-rate mailings for nonprofit groups.

In addition, the administration is proposing to rescind $300 million from the public-service subsidy in this fiscal year. Bolger has said he wouldn't eliminate Saturday mail delivery or other services but would attempt to offset through measures such as productivity gains. The postal service had no comment on the cuts yesterday.

In its rate case the Postal Service had requested a $3.75 billion increase in mailing costs, but the commission approved $2.7 med a $3.75 billion increase in mailing costs, but the commission approved $2.7 billion.

"This is not cost-cutting. It is make believe." Hardesty said. "As every American family knows only too well, costs and obligations that are ignored do not go away."

A few commission recommendations won't go into effect. For example, the governors said they didn't act on a proposal to increase mailing costs for time-sensitive periodicals such as Time and Newsweek by 2.4 cents per magazine.