The Carter administration announced yesterday that a second processing center for Cuban refugees will be opened at Fort Chaffee Army Reserve base near Fort Smith, Ark.

Pentagon officials said the first refugees could begin arriving at Fort Chaffee by this weekend, relieving the already overburdened processing center at Eglin Air Force Base in the Florida panhandle.

The tide of refugees reaching Key West, Fla., hit a single-day high of 4,000 on Tuesday, lifting the number of Cubans reaching the United States by boat in the last two weeks to more than 20,000.

To deal with mounting problems caused by continuing exodus, the administration dispatched 400 Marines to Key West to help National Guardsmen already on duty there maintain order.

At Key West, thousands of refugees were temporarily housed in a Navy airplane hangar, vacant buildings and an abandoned missile site.

Almost 5,000 more refugees were at Eglin, many of them already processed by federal officials and awaiting only final clearance from Washington before they could leave for resettlement.

Pentagon officials said that Eglin eventually should be able to handle about 10,000 refugees, but that the Cubans came so rapidly that the Eglin facilities were quickly strained.

See REFUGEES, A13, Col. 1>

Fort Chaffee, which was used in 1975 and 1976 as a processing center for some of the more than 50,000 refugees from Southeast Asia who fled to the United States, eventually will be able to handle about 15,000 refugees, officials said. Newly arrived Cubans are to be flown there from Key West as soon as the Fort Chaffee facilities are ready, they said.

Officials in Key West said many of the newly arriving refugees had been released from Cuban prisons, and that large numbers of the fleeing Cubans were diseased.

We've seen literally everything in the book," said Sgt. Jeff Mayo, a medical specialist with the Army Special Forces. "We've had a fair amount of active tuberculosis -- between 35 and 50 I'd say -- and a lot of veneral disease, including herpes, syphillis and a lot of gonorrhea."

While officials sought to deal with the immediate emergency needs of the refugees, the administration's long-term policy toward the Cubans -- and the thousands of refugees from Haiti who have also arrived by boat in south Florida -- was no clearer.

Jack Watson, a senior assistant to President Carter in charge of the refugee problem, said on NBC's "Today" program that the government is "undertaking a massive resettlement effort which will be directed at resettling the refugees in different parts of the country outside of Florida."

Watson did not specify where else the refugees might be resettled. "We are relying and will continue to rely on national voluntary organizations and agencies to assist us on this," he said.

Florida Gov. Robert Graham said on the same program that 35 to 40 percent of the refugees are likely to settle in south Florida because they have relatives among the area's large Cuban community.

In other developments yesterday:

The AFL-CIO urged the administration to accept the Haitian refugees with "the same generous and humane policies" it applies to Cuban refugees. The labor federation's president, Lane Kirkland, said American should welcome not only political refugees but also economic refugees whose plight results from political oppression.

The U.S. Conference of Mayors, in a letter to Attorney General Benjamin R. Civiltet, asked the administration to grant refugee status to all of the newly arrived Cubans and Haitians. Such a classification would make the refugees eligible for federal aid and would mean local governments would be reimbursed by the federal government for services provided to the refugees.

Administration officials have said they are contemplating a "group determination" that the Cubans are genuine political refugees, but no final decision has been made.