The world's food supply is facing a crisis next year as floods, drought and swarms of locusts ravage production areas around the globe, the head of the U.N. Food and Agriculture Organization said here Friday.

"An increase in the areas under cultivation" around the world will be needed, said Edouard Saouma, director general of the Rome-based FAO, following a drought in the United States, floods in Africa and Asia and a locust plague in sub-Saharan Africa."Even if there is no risk in the immediate future of a worldwide food crisis, there is every reason to be concerned for next year," Saouma, told a news conference.

For the first time in 10 years, worldwide grain stocks are set to fall below the level seen by the FAO as a minimum guarantee of the world's food supply, Saouma said.

Grain production should reach 1.968 billion tons in 1988-89, representing a 6 percent fall against the previous year. FAO has predicted a fall in world grain stocks of 119 million tons, a 30 percent reduction and the largest fall ever recorded in a single year.

"The margin of security which the substantial reserves used to provide has now been eroded," Saouma said.

Worldwide grain production will have to increase by 220 million tons - or 13 percent - in 1989 to return stock to the minimum required level, according to FAO forecasts.