U.S. officals here have asked the Cuban government for permission to begin an airlift to the United States of 389 Cubans who fled into the American diplomatic mission yesterday after a bloody clash with alleged Cuban security agents.

Informed sources said the Cubans have not yet replied to U.S. proposals for evacuating those inside the U.S. Interests Section. No details of the type of aircraft or timing of the proposed evacuation were revealed.

"We have no way of telling how long this will take," said one U.S. diplomat who sounded exhausted after a sleepless night. "But there is a desire on both sides to get the thing solved. We are optimistic."

In the meantime, the mission has offered temporary refuge to 308 men, 69 women and 12 children who refused to leave following yesterday's violence. The refugees spent the night in the seven-story mission building together with most of the 20 U.S. employees here.

Several hundred white-helmeted Cuban secruity forces have laid a tight cordon around the building, which stands alone, surrounded by a cement patio and parking lot, overlooking the city's main waterfront boulevard. The blinds of the building are drawn, its doors are barred and its ground floor windows covered with paper.

There is little doubt that Cuban authorities provoked yesterday's incident, when at least 20 club-wielding men attacked without warning a group of about 800 Cubans waiting outside the building for U.S. visas. The attack and ensuing stone-throwing melee between the two sides were witnessed by U.S. officials and American reporters.

Today, the Communist Party newspaper Granma published a front-page editorial blaming the violence on "Yankee provocation" and fiercely attacking the mission staff.

But the Cuban government has not permitted a repeat performance of last month's events at the embassy of Peru.

On April 4, the Cuban government provoked a rush on the Peruvian Embassy by announcing it had removed all police protection. Within 24 hours, more than 10,000 people, by Peruvian count, had jammed into the compound looking for political asylum and hoping to leave Cuba. Of those 10,000, only 500 are still inside the embassy --the rest have either left the country by boat or returned home with government assurances they can leave.

Cuban and foreign reporters have not been allowed through the barricades surrounding the U.S. mission, but the American staff has been free to come and go and has brought food and drink for the crowd inside.

"We went and bought food. There is little but enough to feed everyone," one U.S. diplomat reported by telephone.

The men, women and children are being kept on the reasonably spacious groung floor of the building. According to U.S. staffers, they slept on pieces of cardboard on the marble floors, on chairs, or "on whatever soft things they could find."

So far, there have been none of the signs of violence and chaos that arose inside the Peruvian mission, where most of the refugees were outdoors within fenced-in compound. "Until now, they have behaved admirably," reported U.S. information officer Robert Jordan. "They have formed committees to take care of food distribution, of the cleaning and of the sleeping arrangements."

Last night and much of today, the crowd watched movies, including a documentary of the Winter Olympics.

There are still 14 wounded Cubans inside the mission. The four persons who have severe head wounds are being kept at an improvised infirmary in the building. One may whose life was believed endangered by internal hemorrhaging was taken to a local hospital accompanied by an American official who assured the patient he would get the same departure treatment as those inside the embassy.

The mission staff worked through much of the night, some of them manning an open telephone line with Washington, others issuing documents for the refugees to enter the United States.

Many of those Cubans inside are among the 4,000 former political prisoners who had registered with the U.S. mission when they became eligible for American visas under new U.S. refugee legislation.

By this afternoon, about 250 people inside had been processed, according to a U.S. official. "We are seeing how many people are eligible and what for. Many already have Cuban travel documents, some have dual nationality, some had applied for immigration visas," he said.

Several of the former political prisoners inside said in an earlier interview that they had served long sentences, in some cases 10 years and more, for acts of sabotage and other "counterrevolutionary activities."

The Cuban government, which officially holds the U.S. mission responsible for yesterday's incident, has not issued any statement of regret.

Diplomats here now offer two possible explanations on the clash.

One, reportedly also put forward by a high Cuban official, was that security forces had been erroneously told that there was a riotous crowd outside the U.S. mission building that was turning into an anti-Castro demonstration. The security agents were then ordered to go and break it up. "Someone made a mistake somewhere along the line I think," the high Cuban official reportedly said.

The other scenario is that Castro, who has stepped up his campaign to recover the U.S. naval base at Guantanamo, has not only cornered the United States over the flow of refugees from the port of Mariel but now also filled the American mission and is forcing Washington to negotiate.

The people who credit this explanation point out that nothing as significant as sending security agents to the American mission could happen here without clearance from either Fidel Castro himself of his brother Raul.