The Civil Aeronautics Board gave the nation's airlines authority yesterday to raise their basic fares to cover rapidly rising fuel costs. The action will mean a 4.5 percent increase in the cost of most airline tickets.

The CAB said fares can go up to 9.5 percent above their ordinary base levels. Since the board earlier allowed -- and most airlines imposed -- an up to 5 percent increase above the base rate, the action translates into a 4.5 percent increase for most airlines.

Under the new order, which is effective Saturday, carriers can file for higher fares on a 24-hour notice. Some filings are expected on Tuesday after the Labor Day weekend.

The CAB had not planned to review the ceiling fare level until Oct. 1, but said the ballooning cost of aviation fuel necessitated the early action.

The board had estimated that fuel prices would average aboue 51 cents a gallon through September. But in July they went up from 52.5 to 59 cents a gallon. That's a jump of 11 percent, the highest for any month this year.

The CAB also approved Pan American World Airway's proposals to raise its international discount fares by up to 10 percent and to offer a new business class of service while cutting economy class fares.

The up-to-10 percent increase, which the airline linked to escalating fuel costs, will affect service to Europe and some other markets not including Japan and South America. Trans World Airlines similarly will increase its discount fares to Europe. Both increases will be effective Sept. 15.