Bolivia’s embattled president, besieged by protests, abandoned by allies and facing evidence that his party rigged the presidential election last month, called Sunday for a new vote in an extraordinary concession aimed at calming the public’s fury.
The proposal, however, did not placate demonstrators or leaders of the opposition, who are demanding that President Evo Morales step down and not stand for re-election in the most significant threat yet to his efforts to hold on to power.
“Mr. Evo has ruptured the Constitutional order — he needs to leave,” Luis Fernando Camacho, one of the main leaders of the protests, said.
Carlos Mesa, the former president who came in second in the disputed election in October, said the country’s political parties should come together and organize a new vote. He also blamed the president and his vice president on Sunday for “this FRAUD and the social unrest that has led to several deaths and hundreds of people wounded.”
Mr. Morales, who was the first president of Indigenous descent in a country where two-thirds of the population is Indigenous, has been in power longer than any other head of state in Latin America. He had been facing growing challenges from the opposition, which had accused him of illegally changing the Constitution so he could run for an unprecedented fourth term.
That pressure increased exponentially after last month’s disputed elections. Demonstrations calling for him to step down and allow for new elections peaked on Saturday, when groups of police officers across the country broke ranks with the government and joined anti-government protests.
Mr. Morales appeared to be quickly losing his grip on power over the weekend. He called on Saturday for political dialogue to restore order, but the main opposition leaders rejected the overture, saying his departure was the indispensable first step to ease the crisis.
Speaking in a televised address on Sunday, Mr. Morales called for peace and said he would replace the Electoral Tribunal and hold a new vote, without specifying a date. The opposition had criticized the tribunal for its bias in favor of Mr. Morales, and it had been accused of widespread electoral fraud.
This new election would be a “vote that will allow the Bolivian people to democratically elect their new leaders, incorporating new political actors,” Mr. Morales said from El Alto. “I want to ask everyone to lower all the tension.”
But his offer to hold new elections appeared to not satisfy demonstrators.
Martha Yujra, a member of a workers union in El Alto, the municipality adjacent to La Paz that has been a traditional Morales stronghold, said Sunday that protesters will remain in the streets until Mr. Morales steps down.
“He has to resign,” she said. “He can’t call for a new election.”
Mr. Morales’ speech came hours after the Organization of American States, the main entity that monitored the Oct. 20 election, released a preliminary report outlining widespread irregularities. It said the election ought to be annulled.
The O.A.S. report bolsters the widely held view among Bolivians critical of Mr. Morales that the president and his allies, facing the toughest electoral battle since he came to power in 2006, engaged in a concerted effort to rig the vote.
Election officials said Mr. Morales received slightly more votes than he needed on Oct. 20 to avoid a runoff. But the legitimacy of that victory was called into question almost immediately because that finding contradicted early results, which showed he had not won by more than 10 percentage points, the threshold needed for a runoff.
The company that provided vote-counting machines for the election had also disavowed the results.
By Saturday night, the unrest had spread to Mr. Morales’s stronghold of El Alto, where government supporters and protesters clashed on the streets, according to local news reports.
In the countryside, where Mr. Morales remains popular with poor farmers, government supporters blocked and attacked with stones several caravans of protesters heading to demonstrations in La Paz.