Federal drug agents in Miami yesterday arrested the prime minister and two other officials of the tiny Turks and Caicos Islands, a British colony just southeast of the Bahamas, after they allegedly promised undercover agents that they would provide a safe haven for planes carrying cocaine and marijuana from South America to the United States.

Peter Gruden, special agent in charge of the Miami office of the Drug Enforcement Administration, said that Prime Minister Norman Saunders and the other suspects were arrested about 3:30 p.m. at a Ramada Inn near the Miami International Airport as they met with a DEA informer and an undercover agent posing as a drug trafficker.

According to Gruden, drug-trafficking has been conducted in the Turks and Caicos Islands "for a period of years." He said he expects additional arrests in the case.

He said that although foreign officials previously have been indicted on drug charges, Saunders and the other officials of the Turks and Caicos Islands were the first lured into U.S. jurisdiction for arrest.

The men will be charged with racketeering and conspiracy to import cocaine, Gruden said. A DEA official said the two counts each carry maximum penalties of 15 years in prison and a $25,000 fine.

The Turks and Caicos Islands, a group of 42 small islands with a population of about 8,000 in the British West Indies, has been suspected of being involved in the drug trade because of its convenient location as a stopping point for small planes on their way from Colombia to the southeastern United States.

The islands have developed a reputation in recent years, because of their bank secrecy laws, of being a haven for persons attempting to hide or launder money.

John Walker, chief of enforcement for the U.S. Treasury Department, has estimated that tens of billions of dollars in tax fraud, drug and other illegal profits flow through offshore banks in places such as the Turks and Caicos Islands, with strict bank secrecy laws.

Miami DEA agent Frank Chellino said that there had been a number of meetings between the drug suspects and undercover agents in Miami and elsewhere, and most were recorded by videocameras and tape equipment. One major purpose of the meetings, Chellino said, was to discuss payoffs for officials of the Turks and Caicos Islands.

Besides Saunders, 41, who has been prime minister since 1980, those arrested included Stafford Missick, 47, minister of commerce and development for the islands, Aulden Lee Smith, 33, a member of the island legislature, and Andre Fournier, a businessman from Sherverooke, Canada, who was to provide the cocaine for the operation.

DEA officials said that Saunders previously received a $30,000 payment for his support in the scheme and was given $20,000 more at yesterday's meeting. The other officials received smaller sums at yesterday's meeting, the officials said.

Chellino said the three officials were in Miami on personal business and were not covered by diplomatic immunity. He also said that the DEA had kept the British government informed throughout the investigation and received cooperation from Turks and Caicos police.

DEA sources said the men who were arrested had been involved in at least one shipment of cocaine into the United States. These sources said that the investigation had continued for months.

Chellino said the meeting was held to complete plans for a "multi-kilo shipment of cocaine." He said Saunders and the others agreed to provide a landing strip and refueling services for planes smuggling drugs from Latin America, along with protection from island customs and law enforcement authorities.