LOS ANGELES, JULY 10 -- An unprecedented surge of interest in taking drinking water from the sea along the drought-stricken California coast culminated today with initial approval of what would be the nation's largest distillation plant. It could produce 5 million gallons of water daily to ease Southern California's chronic shortage.

The board of the Metropolitan Water District (MWD), the region's largest water agency, unanimously agreed to a $500,000 study to determine the best site for the $30 million plant.

The action came as several California cities, caught in the state's worst drought in 60 years, indicated interest in new desalination methods being used in the Middle East and south Florida. "At some point in time, I don't know when that is going to be, desalination will be the answer to our water problems in Southern California," said Gary M. Snyder, MWD's assistant chief engineer.

Most cities have declined to use desalinated water because of its great cost. Water from the proposed MWD plant, although powered by waste heat from an existing power plant, would cost $1,000 per acre foot or 0.4 cent per gallon, four times the current cost of water from rivers and runoff from the Sierra Nevada mountain range.

But new demands on those traditional water sources are expected to increase their cost, and many California businesses and developers appear willing to pay a premium for a steady supply of desalinated sea water.

On tinder-dry Catalina Island, 26 miles off the Southern California coast, a development company named Hamilton Cove Associates has agreed to build a $3 million desalination plant producing 132,000 gallons daily to win permission to complete a condominium project on the island.

The city of Santa Barbara, where drought police are ticketing people who water lawns and some homeowners are painting dried grass green, is considering more than 20 proposals to purify ocean water. North of San Francisco, Marin County is beginning a three-month test of a device that could make brackish Bay water drinkable. Several other water districts are collecting information on desalination.

Water engineers here said they expect California to join Saudi Arabia, Kuwait and some parts of south Florida on the growing list of rich coastal areas that have more money than water and are willing to invest millions to keep taps flowing and economic growth continuing.

Oil-rich Saudi Arabia has 22 desalination plants capable of producing 550 million gallons of water each day, about one-fourth of the total world production of desalinated water. Japanese companies have built many Middle Eastern plants, although Israel constructed one of the first major sea water distillation plants in the desert town of Eilat in 1965.

In the United States, much research on desalination has been driven by the need to meet new water-quality standards and provide pure distilled water for the electronics industry. But residential booms in areas of Florida and California with few remaining water sources have brought the technology to municipal water departments.

Jack Jorgensen, executive director of the National Water Supply Improvement Association in St. Leonard, Md., said Florida's current daily production of 50 million gallons of desalinated water will jump to 250 million gallons in 1992 when several projects are completed.

Despite the cost, communities are finding the converted sea water convenient, particularly since "you can locate the plants at close proximity to the potential users," rather than arrange for pipeline transport from mountains and rivers hundreds of miles away.

Most plants separate salt and other impurities from water in one of two ways. One method, sometimes called "reverse osmosis," forces sea water through a special membrane that filters all but water molecules. The other method, distillation, heats sea water to create unadulterated steam, which cools to become distilled water.

The membrane method is used in the electronics industry, most south Florida plants and the Marin County experiment and works best with bay water or waste water not as salty as sea water. Larger plants, such as those in the Middle East and the proposed MWD plant, find the distillation method more efficient.

Jorgensen said membrane research has produced advances. In 1992, the nation's largest desalination plant is to open in Yuma, Ariz., using the membrane method to purify 72 million gallons daily of brackish irrigation water for shipment to Mexico under an agreement on use of the Colorado River.

If work proceeds as planned, Snyder said, MWD could open its desalination plant in three years and use it as a guide to building much larger plants. The plant would take in 25 million gallons of ocean water daily, remove 5 million gallons of fresh water and return the rest to the sea with its salt content increased from 3.4 percent to 6.4 percent and its temperature raised from 61 to 74 degrees.

Snyder said studies indicate no significant environmental damage from the process. Eventual construction of a much larger plant, capable of producing 100 million gallons daily, probably would require a new power plant fueled by oil, coal or nuclear energy, which MWD officials acknowledge might be opposed by nearby residents and environmentalists.