While the Carter administration continues to search for a way to finance the resettlement of Cuban exiles in this country, anxious members of Congress have begun to act.

"I do not believe we can wait," Rep. Dante B. Fascell (D-Fla.) said Wednesday as he proposed legislation to ensure that state and local governments will be reimbursed for the cost of aiding the newcomers, who now total in excess of 110,000.

Sen. John Neinz (R-Pa.) introduced a resolution earlier in the week calling on President Carter to designate the Cubans as "refugees" so that the federal government will pick up the bill for most resettlement expenses.

Fascell, Heinz and other members of Congress from states where the Cubans are being processed in military centers have been deluged with calls from local officials concerned about the financial burden of providing for the exiles.

A Fascell aide pointed out yesterday that 20,000 additional Cuban or Haitian children are expected to be enrolled in Dade County, Fla., schools this fall, and that language training will cost $1,000 per student.

An aide said Heinz introduced his resolution to force some action by the administration. Administration officials have delayed a decision on the ultimate status and benefits to be made available to the Cubans, searching for a way to furnish some money without creating a precedent that would encourage another rush to U.S. shores.

The 1980 Refugee Act, Heinz urges, would satisfy the state and local goverments because it means full reimbursement, but it might be a magnet for future mass migrations.

Administration officials fear that trying to pass speical legislation in an election year will be even more difficult.

Thus far, the Cubans are being treated as applicants for asylum, not as refugees, and the funding for opening the processing centers originally was taken from the federal disaster relief fund.

That action angered Sen. Quentin Burdick (D-N.D.), whose public works subcommittee oversees the disaster fund.

"That money is meant for natural disasters -- floods and tornados -- not social disasters," an aide to Burdick said.

The administration's task in finding the right vehicle for financing the Cuban resettlement effort is complicated further by warnings such as the one recently voiced by Sen. Walter Huddleston (D-Ky.), who wants to limit the number of immigrants entering the country each year to 650,000.

Under this plan, every Cuban admitted to the United States in the boatlift would necessitate cutting the quota for legal immigrants.

Huddleston said he plans to attack appropriations for the Cubans until his plan is acted upon.

In other developments yesterday, the flow of boats from Cuba's Mariel harbor to Key West, Fla., dwindled. Arriving boat captains reported only about 30 vessels remaining in the harbor.

One shrimp boat contained 220 Cuban newcomers, three-fourths of whom were convicts, according to a U.S. Customs official in Key West.

Meanwhile, the White House issued a belated statement in which President Carter said the captain of the freighter Red Diamond V and the Cuban Americans who chartered it would be prosecuted vigorously.

"There should be no misunderstanding of my intention" about stopping the illegal boat traffic, the president said, regardless of the nation of registry. The ship was under the Panamanian flag until its registry was revoked Monday at the State's Department's request.

The freighter arrived Tuesday with 731 refugees aboard.