President Carter declared portions of south Florida a federal disaster area yesterday as Cuban refugees continued to pour into that area and the administration continued to grope for a long-term policy to deal with the thousands of new arrivals.

Victor Palmieri, ambassador-at-large for refugee affairs, said the administration was considering making a "group determination" that the fleeing Cubans are genuine political refugees, making them eligible for federal assistance for two years.

But Palmieri and other officials said decisions on the final status to be granted the refugees will depend on such factors as the extent of the exodus from Cuba, the likely cost to the United States and the outcome of consultations with Congress.

In the meantime, the officials said the immediate problem was to deal with the humanitarian problems presented by the tide of refugees, who continued to pile up at their arrival point in Key West, Fla., in Miami and at a special processing center hastily established at Eglin Air Force Base in the Florida panhandle. By late yesterday, White House officials estimated their numbers at over 18,000.

The disaster declaration that Carter signed yesterday makes the state and local governments in Florida eligible for reimbursement by the federal government for "extraordinary costs" incurred in dealing with the refugees. Officials had no estimate of how much this will be, but noted that in the first week of the boat lift out of Cuba the costs to the Florida state government and Dade County (Miami) were estimated at $600,000.

In addition, the president has authorized up to $10 million from the refugee emergency fund to establish the processing center at Eglin and to begin the resettlement process.

The mass migration, which began two weeks ago when Cuban President Fidel Castro announced that people wishing to leave the island were free to board boats for the United States caught the Carter administration off guard.

Initially, the administration discouraged owners of small boats, many of them considered unsafe in the open sea, from traveling to Cuba to pick up refugees. The administration wanted the migrants sent in a more orderly way, and not all here and altogether at Castro's whim.

But on Monday, answering a question before the League of Women Voters convention, the president switched signals, saying the refugees would be welcomed to the United States with "an open heart and open arms."

Describing the problem confronting administration policymakers, White House press secretary Jody Powell said yesterday.

"We will not tow boats back to Cuba. On the other hand, the United States of America cannot become a place of residence for everyone in the world who wants to come here. Those are the horns of the dilemma."

Boat owners delivering refugees to Key West are no longer automatically fined $1,000 for each refugee. However, Powell said boat owners are being issued citations, giving the government the option to levy fines later. He said the government will come down hardest on operators of unsafe boats and "those who are in this just to make a buck."

At the State Department, spokesman Hodding Carter said the administration hoped to "nationalize" the refugee problem by resettling many of the Cubans outside of Florida and to enlist the agreement of Latin American countries to accept some.

U.S. and Latin American officials will meet tomorrow in Costa Rica to discuss the problem.

The president met yesterday morning with members of the Florida congressional delegation. Afterward, one congressman predicted that as many as 250,000 Cubans and another 250,000 Haitians would eventually migrate to the United States, but White House officials said there was no way to know the extent of the exodus.

According to Palmieri, the Cubans reaching Key West are being accepted as "applicants for asylum." If determined to have a well-founded fear of persecution if returned to their homeland, they would be granted refugee status, making them eligible for aid and eventual U.S. citizenship.

Normally, these cases would be decided on an individual basis, but Palmieri indicated some overall determination of the Cubans' status may have to be made.

He also said that the administration is making no distinction between the Cuban refugees and the thousands of Haitians who have reached south Florida by boat in recent weeks seeking refuge from what they called political persecution.

Beyond the immediate humanitarian aspects of the problem, administration officials said they are seeking "a safer and more orderly way" to bring the refugees out of Cuba. Palmieri suggested an airlift as one possibility, nothing that "it's happened before" but would require the cooperation of the Cuban government. He said he did not think this had been discussed with Cuban officials.