In Bolivia, the president’s pleas for peace have done little to quell the violence.

In recent days, evidence has mounted that Mr. Morales’ party rigged last month’s presidential election. But even before the vote was cast, the opposition was accusing the president of acting illegally by changing the Constitution so he could run for an unprecedented fourth term.

The Organization of American States, which monitored the Oct. 20 election, issued a preliminary report on Sunday that outlined irregularities and said the vote should be annulled.

Carlos Mesa, the former president who came in second in the disputed election, has said that the country’s political parties should come together and organize a new vote. On Sunday, he lashed out at the president and the vice president on Sunday for “this fraud, and the social unrest that has led to several deaths and hundreds of people wounded.”

Michael Kozak, the top diplomat at the State Department overseeing Latin America policy on Sunday endorsed the call for a new election. “All those implicated in the flawed process should step down,” he wrote on Twitter, without addressing the question of whether Mr. Morales should be eligible to run again.

Demonstrations calling for the president to step down and allow for new elections appeared to reach critical mass on Saturday, when groups of police officers across the country broke ranks with the government and joined anti-government protests.

In his televised address Sunday, Mr. Morales called for peace and said he would replace the Electoral Tribunal and hold a new vote, though he did not specify a date. The opposition had accused the tribunal favoring Mr. Morales and taking part in election fraud.

Mr. Morales said the new election would be a “vote that will allow the Bolivian people to democratically elect their new leaders, incorporating new political actors.”