Cuba has notified the United States for the first time that it is imposing stiff prison sentences on airplane hijackers, and the Federal Aviation Administration said yesterday that it would cite the Cuban crackdown in a new campaign against air piracy.

Responding to longstanding U.S. requests, the Cuban government summoned a representative of the U.S. interests section in Havana late at night "on a rather urgent basis" to deliver a diplomatic note. The note showed, case by case, how skyjackers landing in Cuba from the United States since 1981 have been given sentences averaging 15 years.

The same note showed that until 1981 hijackers received sentences ranging from two to five years, according to officials from the State Department and the FAA.

The Cuban diplomatic note was delivered June 15, a day after the most recent skyjacking from South Florida to Havana. So far this year, five U.S. flights have been diverted to Cuba, four in one seven-week period.

"After every hijacking we send the Cubans a note, and for years we've been asking for an accounting of what they've been doing" with the hijackers, said Mayer Nudell, a staff member in the State Department's Office for Combatting Terrorism. "We've been hoping for some kind of response. This is a first step."

John Leyden, an FAA spokesman, said:

"We are making an effort to make clear that any homesick Cuban who hijacks a plane is not going to be reunited with his family but faces an almost certain prison sentence. Most of these recent hijackings have been homesick Cubans, you could say."

"The evidence is quite clear that they're being much tougher than they used to be," a State Department official said, "and that should reduce the number of hijackings--that is, if hijackers are rational.

"Once they're aware of the punishment they may get for this, it should have a deterrent effect." The FAA also announced yesterday that it has made mandatory the "extraordinary screening measures" which until now have been voluntary in South Florida airports, and that armed air marshals will resume riding selected flights.

The State Department yesterday offered no explanation of why the government of Fidel Castro, which has treated the sentencing of hijackers as an internal affair, suddenly changed its mind.

Until now, the U.S. government had no way of knowing how the Cubans treated air pirates.

"Sometimes when a person turns up on the street," said one State Department official, "you know he's not in jail in Cuba, but mostly we have to rely on what they tell us."

The treatment of hijackers has been one of many longstanding disputes between the United States and Cuba. In 1973 the two nations signed a bilateral agreement calling for sky pirates to be returned to the nation they left or punished at their landing point.

Cuba has generally honored the agreement, officials said, despite denouncing it in 1976. But Cuba has treated all specifics of the trial and punishment of air pirates, including their identities, as a private matter. Even in 1980, when seven planes were hijacked in two months, the Cubans refused to budge from their policy of nondisclosure.

Cuba's June 15 note, cooperative in substance, was "dipped in acid," an official said.

Its tone reflects ongoing tensions between the two countries, in particular those over U.S. requests for the repatriation of Cuban entrants from the Mariel boatlift of 1980. Some of the Cuban emigrants have been reported to be eager to return home, but Havana has refused to take them.

If Cuba relented on this issue, Nudell said, "this would diminish the necessity for people to hijack airplanes."