Chilean police reported that six persons were killed and 567 arrested in protests yesterday and early today against the military rule of President Augusto Pinochet.

The protests were called by the formally banned Communist Party to mark what had been Chile's traditional election day, Sept. 4. Next Wednesday, the 12th anniversary of the coup led by Gen. Pinochet, is also expected to provoke protests.

While left-wing activists clashed with the paramilitary national police, most Chileans appeared to heed the call by the more centrist opposition forming the Democratic Alliance to stay home. The group formally opposed demonstrations, apparently foreseeing violence.

The Democratic Alliance instead proposed that Chileans sign statements of support for unrestricted elections. Eleven political parties, from the left to the far right -- but not including the Communists -- issued a plea Aug. 26 for a return to civilian rule through elections.

The only violence in downtown Santiago yesterday occurred when police used tear gas and water cannons to disperse a large crowd gathered to sign the statements of support for the coalition's proposal.

Otherwise, the inner city seemed virtually deserted. Shopkeepers stayed home -- either in protest or in fear -- and taxi and bus service in the center city was sporadic and by evening almost nonexistent.

Most of the violence occurred in the slums that ring Santiago and at universities. Protesters erected barricades of burning tires and heaved rocks and molotov cocktails at police.

Roman Catholic Cardinal Juan Francisco Fresno called off a memorial mass at the main cathedral for a French priest who was killed by a random bullet during antigovernment protests last year. The cardinal said the mass could erupt into violent demonstrations against the 12-year military rule.

But the mass was held nonetheless in a church in the slum where the priest worked. Afterward, chanting crowds erected barricades and heaved rocks at police, who responded with tear gas. Protests were reported in Chile's other cities, but the killings occurred here.

Interior Minister Ricardo Garcia said today that the government would bring legal action against the organizers of the protest. By dawn today, downtown Santiago had returned to normal, although clashes continued in some slums and schools.

Police said six persons were killed and eight wounded, five of them seriously, by gunfire. A police statement said, "This institution did not use firearms in any sector to break up disorders," and officers blamed unknown gunmen. In one case, witnesses said a fatal bullet appeared to have been fired by police.

Eighteen police were wounded, apparently none seriously, according to officials. Extensive looting was reported in several cities.

Reacting to the violence in a speech Wednesday, Pinochet said, "We find ourselves confronted not with a harsh dictatorship but rather with a gentle dictatorship. But if it becomes necessary, we will have to tighten the grip."

Pinochet's rule came under attack last year, provoking the proclamation of a state of siege. Political pressure revived last month after the head of the police was forced to resign from the four-member ruling junta.

A government prosecutor had named a dozen police in the slayings earlier this year of three Communists. On Aug. 2, the day after the prosecutor's report was released, Gen. Cesar Mendoza became only the second member of the junta to resign in 12 years.

Mendoza was replaced by Gen. Rodolfo Stange, who dissolved the special counterintelligence unit in the police force.

Chileans and diplomatic observers said yesterday's protest was the most intense since last November. The state of siege, with its strengthened police powers, was lifted earlier this summer under strong U.S. pressure.

The 11-party call for elections was initiated at a meeting called by Cardinal Fresno in early August. Fresno previously had kept a low political profile, and his role in bringing together noncommunist opposition politicians represents a changed role for him and the church.

According to the constitution written under Pinochet's tutelage, the armed forces are to choose a successor in 1989 for an eight-year term, subject to a referendum.