SANTO DOMINGO, Dominican Republic (AP) _ U.S. Attorney General Edwin Meese III gave two confiscated high-speed boats to military authorities here Wednesday for use against drug traffickers.

Smugglers use this Caribbean island nation as a transshipment point for cocaine coming in from South America and bound for the United States.

''The Dominican Republic seems to be determined ... that narcotics trafficking should be totally eliminated,'' Meese told Gen. Antonio Imbert Barrera, the armed forces minister.

He made his remarks as he and other officials from the United States and the Dominican Republic stood near the long, sleek boats, capable of speeds of more than 65 mph.

The Dominican Republic shares the island of Hispaniola with Haiti. Drug runners have turned to the island as governments on the neighboring islands of Jamaica and Puerto Rico tightened surveillance of boats and planes.

President Joaquin Balaguer, elected to a fifth term in May 1986, has made the war on drugs a top priority. In December 1986, the Dominican air force shot down a small plane that did not identify itself upon demand. Officials later said it was carrying hundreds of pounds of cocaine.

In recent months, police and soldiers have seized cocaine shipments weighing hundreds of pounds and valued at millions of dollars. But suspected smugglers in high-powered boats often outran the patrol boats of the Dominican coast guard.

''These (confiscated boats) are going to put the Dominican Republic one step ahead of the smugglers,'' one U.S. official said, speaking on condition of anonymity.

The boats were confiscated from traffickers apprehended while trying to smuggle drugs into the United States, he said.

One is a 31-foot Chris Craft Scorpion with twin 235 horsepower Mercury engines and the other a 33-foot Sonic Carrera 33RX, he said. The value of the boats, delivered from Florida by U.S. Coast Guard C-130s, was not disclosed.

The United States also plans to supply five small, twin-engined Cessnas to the Dominican air force under the Military Assistance Program.

Accompanying Meese were his wife Ursula; the chief of the Drug Enforcement Administration, John Lawn; Frank Keating, the Treasury Department's assistant secretary for enforcement; Mark Dion, the State Department's deputy assistant secretary; and Mike Skol, director of State's Office of Andean Affairs.

The stop in Santo Domingo was Meese's first in a Latin American tour that began Wednesday.

Meese arrived by Air Force jet and was due to leave Santo Domingo on Thursday.

On Wednesday, Meese met with Balaguer at the National Palace, then with Foreign Affairs Minister Donald Reid Cabral.