Cuban exiles who are hardened criminals and those who took part in violent disturbances at Fort Chaffee, Ark., last weekend will not be allowed to settle in the United States, White House press secretary Jody Powell said yesterday.

The Carter administration's tough attitude toward Cuban criminals and rioters has been touched on earlier by other officials in congressional hearings, but Powell's statement yesterday was the first official White House pronouncement on the issue.

The statement seemed designed to reassure the public that the administration is taking strong action against undesirables. At the same time, Powell took pains to point out that only a small portion of the 112,000 Cubans who have entered the country in the last six weeks are troublemakers.

"While Americans are understandably upset with the behavior of a few . . . it would be grossly unfair and a serious mistake . . . to look at all of those Cubans as if they were like the few hardened criminals," he said.

In his statement, Powell said there is evidence that Cuban President Fidel Castro "exported these undesirable elements to the United States in a calculated effort to disguise the fact that the vast majority of those Cubans who have come to this country were and are law-abiding citizens whose only purpose was to seek freedom and reunification with their families."

He called Castro's action a violation of international law but he also acknowledged that there is no sign Castro is willing to take the criminals back.

Powell and Abbe Lowell, a special assistant to Attorney General Benjamin R. Civiletti, said there is legal authority to confine the criminals and suspected rioters until hearings could be held to exclude them from the country.

Lowell noted that about 700 Cubans have been detained so far as hardened criminals or persons whose mental or other medical informities make them excludable under U.S. immigration law. And, 100 or so have been confined for their suspected part in the Fort Chaffee disturbance and more than 50 were transferred yesterday to an Immigration and Naturalization Service detention center in El Paso, Texas, he added.

Even though expedited exclusionary hearings might be completed in a few months, administrative and court appeals could drag out the process for a couple of years, the Justice Department aide said.

In a related development another senior White House official said yesterday that a decision memo with options on how to finance the influx of Cubans should be on President Carter's desk by the end of the week. The Office of Management and Budget already has told the congressional Budget committees costs for processing and resettling the Cubans could amount to $300 million this fiscal year.

The administration has not decided whether to call the newcomers "refugees," however, because of the fiscal implications and the precedent it would set for dealing with other Caribbean exiles.

Members of Congress from states where the Cubans are being resettled want them declared refugees because under that category state and local governments would be reimbursed fully for expenses.