Morales, Latin America‘s longest-standing leader, won the election on October 20 but the vote count had been inexplicably halted for nearly a day.
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Allegations of fraud have led to protests, strikes and roadblocks.
Morales took to Twitter to denounce the police rebellion as a coup.
“Our democracy is at risk due to the coup d’etat that violent groups have launched that undermine the constitutional order,” he wrote, as he called on Bolivians to protect their democracy and constitution.
“Before the international community, we denounce this attack on the rule of law.”
Morales earlier held an emergency meeting with ministers.
Luis Fernando Camacho, a civic leader from the eastern city of Santa Cruz who has become a symbol of the opposition, replied to Morales’s tweet, saying: “We have not come to overthrow a president, we have come to free Bolivia from its dictatorship.”
Camacho plans to lead a march to the government palace on Monday with a symbolic pre-written resignation letter for Morales to sign.
Bolivians rallied again in several cities on Friday.
Reports of police joining the protests added pressure on Morales.
In the city of Cochabamba, the scene of violent clashes, journalists of Reuters news agency reported seeing police officers protesting on the roof of their headquarters in an apparent act of disobedience against the government.
The foreign ministry said in a statement on Saturday the police officers had “abandoned their constitutional role of ensuring the security of society and state institutions”.
In the small town of Vinto, the mayor, who hails from the ruling Mas party was attacked by opposition protesters on Thursday. They dragged her through the streets and assaulted her shouting “murderer”, according to local reports.
The attack followed reports that two anti-government protesters had been killed, alleged deaths which prompted demonstrators to march towards the city town hall.
After hearing the rumours, a crowd marched to the town hall and lashed out at the mayor.