The daily tally of Cuban rafters picked up at sea has hovered at about 1,000 in recent days, the U.S. Coast Guard said.
Tuesday, 188 Cubans were picked up in the Florida Straits by midday.That followed the 1,129 Cubans who were rescued from small boats, inner tubes and makeshift rafts Monday. Similar numbers were rescued over the long holiday weekend.
"The risk is always great. There is a possibility they won't be spotted," said Petty Officer Luis Diaz. "The rafts are very low in the water and it is extremely dangerous."
Diaz said when migrants are taken off their rafts, the Coast Guard marks them with paint and tries to sink them, but they are not always successful.
"Some of the materials used are not made for sinking. Styrofoam and wood - these are items that will not sink," Diaz said.
He said because of all of the variables, the Coast Guard does not know how many are lost.
"We have no idea how many leave, compared to how many are picked up, " he said.
So far in 1994, the Coast Guard has picked up more than 32,000 Cubans attempting to float to Florida.
Meanwhile, talks about immigration policy between the U.S. and Cuban governments were to resume Tuesday afternoon in New York.
Cuban leader Fidel Castro is pressing the United States to grant more than 1,000 visas to Cuban migrants and to acknowledge that a three-decade-long U.S. embargo has contributed to the exodus of Cubans.
The United States, which previously offered 20,000 visas, has come up with a new proposal on increasing the numbers, according to a U.S. official who described the new offer as "flexible."
Cuba on Monday proposed increasing legal immigration to the United States to at least 100,000 people a year, but a State Department official rejected that.
More than 30,000 Cubans have set sail on rafts and boats this year, most of them in the past month. The United States is holding more than 22,000 rafters at the Guantanamo Bay Naval Base in Cuba.
Haitian refugees who are being held with the Cubans at Guantanamo threw rocks at American soldiers Sunday to protest what they see as preferential treatment for the Cubans.
About 50 Haitians breached one of the camp fences when Panama announced it would accept up to 10,000 Cubans to ease the strain on the crowded base, base spokesman Maj. Rick Thomas said.
Until a recent Clinton administration policy change, Cubans were granted almost immediate entry into the United States, whereas Haitian and other refugees had to prove political persecution.
"We're not asking them to leave the Cubans and take the Haitians," said Rolande Dorancy, a Haitian activist in Miami. "We just want the same for both groups."
Panama is the first country to start taking in Cuban refugees in response to Washington's appeal for help to ease crowding at Guantanamo, where more than 22,000 Cubans and 14,000 Haitians are being held.
Military officials said the first flights from Guantanamo to Howard Air Base in Panama could begin this week.
About 300 soldiers were at work Monday building a camp about 25 miles south of Paramaribo, Suriname, for 2,500 Haitians being transferred from Guantanamo. The first 250 Haitians are expected to be flown Friday to Suriname, on South America's northeast coast.