Faced with the cancellation of federal benefits to refugees who have been in the country for 18 months or more, Florida tried a novel solution: it sent letters to all 38,000 Cubans and Haitians affected, listing 10 other states where medical and financial assistance could be available.

But when strapped welfare officials in the other states protested, Florida temporarily retreated. That means on June 1, refugees in Florida who have been receiving from $84 to $119 a month, plus medical aid and food stamps, could be left with nothing.

"The language in the letter to refugees should have been clearer. We weren't asking them to move," said Danny Pietrodangelo, spokesman for Florida's Department of Health and Rehabilitative Services. "Our intent was to point out other options. For instance, if they have relatives in other states."

Florida's controversial action followed a Reagan administration decision to terminate financial and medical assistance to about 100,000 refugees who have been in the United States for 18 months and do not qualify for conventional welfare programs.

Although the administration's regulation was to go into effect April 1, Florida officials said they could not stop the aid until June 1 because of a state law binding rule-making procedures.

Pietrodangelo said state officials are planning to sue the federal government to recover the $10 million Florida has spent for these refugee services since it was notified of the cutback on March 1.

Florida officials contend that refugee assistance is a federal responsibility. Purely because of geography, they argue, Florida's state and local governments have incurred costs of $150 million in refugee services not reimbursed by Washington during the influx of 150,000 Cuban and Haitian refugees in the past two years.

The Carter administration's Refugee Reform Act of 1980 provided special medical and financial benefits for 36 months. The Reagan administration, however, plans to tie refugee checks to states' general welfare programs.

Since Florida doesn't have a general assistance program, Florida welfare officials informed refugees of the states that do.

"We don't have the money and we don't have the program" to absorb the refugee costs, Pietrodangelo said. "One of the major fears is there will be an even greater increase in crime, that the people who become exceedingly desperate will turn to illegal activities," he said.

"We were surprised, but we certainly understand why Florida did it for humanitarian reasons," Karen Meyer, of the Michigan Social Services Office, said. "For the first 18 months, we'd receive the federal reimbursement. But afterward, the refugees would become a liability for our state. And we're not exactly thrilled about that."

"The states unanimously protested the administration's change," she added. "Originally the refugees were recognized as a federal problem . . . . Now they're a state problem. We probably would have done the same thing as Florida."

In a letter to refugees last week, Florida officials named Hawaii, Kansas, Massachusetts, Michigan, Minnesota, New Jersey, New York, Ohio, Rhode Island and Wyoming as the states where special refugee benefits will continue for 36 months.

Four of these states, however, do not provide special programs for some of these refugees, Florida learned later. "We have a $60 million state shortfall against our existing welfare programs," Bob Baird, assistant commissioner for the bureau of income maintenance in Minnesota's welfare department, said. "We are trying to get Florida's cooperation to tell its refugees that Minnesota is probably no better off than any other state."

As an alternative, Florida is seeking most of the impact aid available to all states for limited refugee services, such as assessing employment skills and deterring refugee-related crime. Earlier this week, the state was granted $5 million toward refugee-related expenses. An aide to Florida Gov. Bob Graham labeled it "a start, but we don't know how much of a start."

"A federal cut-off may well force us to consider aiding these unfortunate people to move elsewhere in the nation where federal assistance is available to them," Graham said in a speech to the Florida Associated Press broadcasters. "It is only fair that other states should assume their portion of what is in fact a national burden."