Protesters seeking the downfall of President Jean-Claude Duvalier demonstrated, set fires and looted shops in three of Haiti's troubled provincial cities today, but numerous armed patrols enforcing a state of siege restored order to the capital.

The relative calm in Port-au-Prince appeared to increase Duvalier's chances of retaining his hold, at least for the time being, on the dictatorship started by his father, Francois (Papa Doc) Duvalier, 29 years ago and passed on to the 34-year-old ruler in 1971, diplomatic and Haitian sources said. Preventing disorders in the capital has been regarded as a litmus test for Duvalier's ability to weather the growing challenge to his government that has spread across the island during the past week.

Widespread rumors that Duvalier had fled before dawn yesterday led many Haitian youths into the streets of Port-au-Prince, with small bands looting shops and stoning cars. But police and Duvalier's Volunteers of National Security, popularly known as Ton-Tons Macoutes, prevented crowds from gathering and rioting. Duvalier's early afternoon appearance on national television, designed to demonstrate that he was still in the country, then appeared to dissuade the capital's population from pursuing the disorders, a diplomat explained.

A half dozen persons were killed and about 50 wounded while an unknown number were arrested under the state of siege announced yesterday permitting police to round up youths and hold them without charges. Gunfire popped occasionally during the night across the city's deserted streets. But by late morning today, some stores began to reopen, and market women displayed their fruits and vegetables on the sidewalk as usual.

"We are sitting on a volcano," said a diplomat monitoring the crisis. "It erupted yesterday, and now it is calm. But it is anyone's guess when it will erupt again." Reports from officials monitoring the situation said protesters set fire to buildings in Les Cayes in the southwest, repeating unrest that broke out there earlier in the week. In Gonaives, the central city where recurrent unrest first broke out over food shortages in 1984, protesters looted shops and defied police attempts to get them off the streets, the reports reaching here said.

In Cap-Haitien on the northern coast, police used tear gas to break up a demonstration that broke out before dawn, but the city was quiet for the rest of the day, the reports said. Six persons have been killed in Cap-Haitien this week, three shot and three more trampled by rioting mobs, but there were no reports of shootings today there or in the other troubled cities.

Police and soldiers, continuing a pattern evident throughout the week outside Port-au-Prince, appeared to be avoiding conflict when possible. Witnesses to disorders have reported soldiers standing by to allow protests and, in some instances, pushing back Volunteers for National Security who tried to intervene with rough tactics against the crowds.

Travelers from Cap-Haitien reported encountering more than 20 roadblocks manned by protesters along the main highway without apparent attempts by the police or Army to intervene.

In the capital, however, where two battalions of the president's traditional enforcers are stationed, Volunteers for National Security appeared to be more numerous than police in city center streets. Several youths were seen being hauled away by the blue-uniformed militamen.

In the more relaxed atmosphere of Port-au-Prince, American Airlines restored its daily flight from New York, canceled yesterday. But Haiti Air, the island's flag carrier, announced that it has suspended all flights indefinitely. Haiti Air's principal owner is Ernest Bennett, Duvalier's father-in-law and one of the country's leading businessmen. His daughter, Michelle, exercises strong influence over the president and often gives orders to ministers at Cabinet meetings, according to diplomats here.

Some reports circulating among Haitians and diplomats here said Duvalier had decided to flee the country yesterday in the predawn hours but was turned back at the last moment by supporters arguing that his departure would mean their ruin. There was no way to confirm these reports, with only a handful of family members and close advisers privy to Duvalier and his wife's actions within the heavily guarded presidential palace.

Soldiers who were guarding the palace in battle dress yesterday were withdrawn today, reducing the atmosphere of siege in the city center. But troops remained on guard at the telecommunications center and other key installations.

The 7,500-man armed forces have given no sign of their attitude on the crisis. Two prominent Duvalier opponents, Hubert de Ronceray and Gregoire Eugene, have called for a military coup as a transitional step toward elections and more representative government.

Diplomatic sources said a coup would be a difficult enterprise because Duvalier has organized each command so that it reports individually to him, bypassing chief of staff Henri Damphy. In addition, officers have been chosen on the basis of loyalty to the president and they are discouraged from contact with one another except via the presidential palace, they said.

Duvalier shifted most of the military's key commanders earlier this month. Although he did not announce the reason, diplomatic sources said an unknown number of soldiers and officers were involved in an attempt to organize a coup against Duvalier in November led by an exiled doctor.