At least three persons have died and scores have been injured in the past 11 days in protests against alleged fraud in municipal elections, according to government officials, opposition parties and press reports.

The most serious incidents took place in the central state of San Luis Potosi and the southern state of Chiapas, but demonstrations were reported in six other states.

Activists of the conservative National Action Party and of smaller left-wing opposition parties staged most of the protests. They demonstrated against the inauguration of new mayors who belong to the ruling Institutional Revolutionary Party, known by its Spanish initials PRI, and who they charge won their posts only because of fraud in elections last year.

Protests against electoral fraud are common in Mexico, but these were noteworthy because they erupted in so many places at once and because of the violence associated with several of them. Police apparently were responsible for killing an elderly man while breaking up a demonstration that had turned violent in San Luis Potosi. In Chiapas, accounts conflicted on how at least two persons, and possibly as many as 11, were killed.

President Miguel de la Madrid, in a clear reference to the incidents, appealed to the nation yesterday to keep political protests peaceful. The president said that all citizens must work "to avoid letting physical violence become established as an instrument for the solution of controversies between Mexicans."

National Action, the largest opposition party, charged that the government had used excessive force against demonstrators in some cases. It said that such "repression," combined with a deterioriating economic situation, could lead to social upheaval.

"It is very delicate because the economic crisis is worsening," Gonzalo Altamirano, a member of the Chamber of Deputies and the party's national spokesman, said.

In San Luis Potosi, capital of the state of the same name, about 50 policemen used lead pipes to break up a New Year's Day demonstration against the inauguration of PRI Mayor Guillermo Santos Medina. The police moved against several hundred demonstrators after rocks were thrown and the city hall was set afire, the government said.

A man in his sixties died of blows to his body during the confrontation, and most accounts said that the police had killed him. The state's governor said afterward that the man was killed by a hit-and-run driver.

In a rare display of divisions within the PRI, more than a dozen state and party officials resigned to protest the use of force to break up the demonstration.

In Chiapas, which borders Guatemala, National Action claimed that 11 persons were killed when police dislodged protesters who had occupied town halls in four communities. Most of those killed were National Action supporters, but several were PRI militants who died while helping the police to break up the sit-ins, according to the opposition party.

A senior state government official, Daniel Sarmiento Rojas, confirmed in a telephone interview that two persons were killed on Jan. 2 in the town of Totolapa. But he said both were PRI activists murdered by National Action militants in a personal dispute, and that two suspects had been arrested in the case.