A severe thunderstorm swept through the southern part of the Florida Straits tonight, threatening scores of tiny boats bound to and from Cuba on the "Freedom Flotilla."

The Coast Guard warned vessels to head for safe ports, but many already well in the 90-mile trip apparently were caught in 50-mile-an-hour winds and 10-foot waves.

The storm veered from a northeasterly to a southwesterly direction early in the evening, avoiding Key West but affecting the southern part of the flotilla's route.

Two U.S. Navy ships en route from Norfolk, Va., to help the Coast Guard patrol the straits are not expected to arrive until Sunday night.

"If they are out there, they are in severe trouble," said Coast Guard Cmdr. Samuel Dennis. "This is the kind of weather that causes stark terror in a 30-foot boat."

A similar storm last Sunday capsized more than a dozen boats and claimed the lives of at least four Americans who were sailing to the Cuban port of Mariel to fetch relatives.

The storm abruptly halted the departure of new boatloads of would-be rescuers. But it threatened to further aggravate what has become a disastrous situation for more than 2,000 American boats stranded in Cuba.

Refugees and boat captains arrive here said the five-gallon jugs of water, which sold for $10 in Mariel a week ago, were now going for $90, and tensions were rising between Cuban police and waiting Americans.

The scarcity of food and drink and the possibility of more than a month's delay before their relatives would be released forced 30 boats to return empty form Cuba Thursday after Cuban-Americans had spent thousands of dollars to charter them.

One 55-year-old Maimi man sold his house and small business to get the money to buy a boat and bring his son back from Cuba. The boat sank. Another boat picked him up, but when he arrived in Mariel, his son refused to leave.

More than 8,700 refugees had arrived by tonight -- 1,920 of them in a 24-hour period that ended at 4 p.m. today -- making this the largest influx of Cubans ever into the United States, surpassing by far the 1,000 a week who flew to Florida during the Cuban airlift in the late 1960s and early 1970s.

Airlifts from Key West to a processing center and "tent city" being set up by federal officials at Eglin Air Force Base, near Pensacola, Fla., may begin as early as Saturday.

The scene at the old Navy Base here was chaotic as a hard rain soaked hundreds of arriving refugees.

Dozens of Cubans waited in line at the only two pay telephones, unfolding rumpled scraps of paper with the phone numbers of relatives as far away as California, Detroit and Chicago. Many of the refugees arrived soaked, trembling with cold and seasickness, without even a suitcase. They sorted eagerly through the piles of second-hand clothes and shoes donated by Cuban exiles.

Two men displayed bandaged wounds, and doctors here treated scores of dog bites. The men said Cuban police sicked dogs on them in Mariel as they waited in line to board boats. The police told them they should get used to such treatment, because dogs were used to attack blacks in the Unted States, the men said.

The majority of the new arrivals were men, most of whom said they had relatives in the United States. After a quick meal of mashed potatoes and meat sauce, they took chartered buses to a large processing center in Miami to be interviewed and given political asylum applications.

More than 95 refugees have been detained by Immigration and Naturalization Service officials pending further investigation of their criminal background. But authorities were allowing numerous political prisoners to pass through the processing center.

The problem of receiving so many new arrivals at once was complicated by evidence that many boats -- possibly number in the hundreds -- were dropping off refugees all along the southweastern Florida coast. U.S. officials have designated the former Key West naval base as the only legal disembarkation point.

Dennis said the problem was "significant" and that 20 border patrol agents were trying to control the illegal landings.

However, he speculated that the boat captains were not seeking to avoid potential penalties for carrying refugees into the United States. "They've had a miserable time in Mariel and they want to get home as soon as possible," he said.

The border patrol seized one boat at Marathon, Fla., and arrested three Cuban exiles, charging them with attempting to smuggle illegal aliens into the United States. They were the first arrests since the boatlift started about two weeks ago, though other boats have been seized. The 10 Cuban refugees aboard the boat were escorted to Key West to join other refugees being processed here.