Police in at least three Bolivian cities have declared mutinies and joined anti-government protests – a possible indication that parts of the security forces may be withdrawing their backing for President Evo Morales after weeks of unrest over disputed election results.

Bolivia’s defence minister, Javier Zavaleta, said on Friday that no military action would be taken against the police involved for now and the government would not mobilise troops as tens of thousands of Bolivians took to the streets in cities across the country.

The commander general of the Bolivian police said the officers had been “garrisoned” and had not mutinied.

Television images showed thousands of protesters gathered in peaceful vigils throughout the night at police stations and army barracks. More began to arrive at sunrise on Saturday morning.

Bolivia’s interior minister, Carlos Romero, said in a televised address that a “coup strategy was taking place” and hinted that talks could take place to try to resolve the escalating political crisis as protesters call for Morales to step down amid accusations of fraud in October’s presidential elections.

In La Paz, crowds cheered dozens of police officers who marched down a main avenue and garrisoned themselves in the city’s central police station. Other police remained on the streets guarding barricades around the presidential palace on Friday but the mood was starkly different from previous nights of clashes as protesters surrounded them singing: “Brother, police, join the people.”

In the rest of the country, police units in the official capital, Sucre, and the most populous city, Santa Cruz, a bastion of the opposition, announced they were joining a mutiny launched by police officers in Cochabamba. Uniformed police waved Bolivia’s red, yellow and green flags from the rooftop of their station in Cochabamba. Local reports showed protesters picketing police stations in other cities urging officers to join them.

At least three people have died, the latest a 20-year-old student on Wednesday, in clashes between anti-government protesters and Morales’ supporters since the disputed election on 20 October.