The opposition has been demanding Morales' resignation and fresh elections.
Police in Sucre "are joining in support of the comrades who have mutinied in Cochabamba", a uniformed officer, his face covered, told local TV from the door of a police station. He asked the Bolivians to protect their democracy and constitution.
"Sisters and brothers, our democracy is at risk due to the coup d'etat that violent groups have launched to undermine the constitutional order", he wrote on Twitter late on Friday.
Carlos Mesa, the main opposition leader and a former president, promptly rejected the suggestion.
Addressing Morales in a video message, Mesa suggested he should step down.
Police units in some cities started protesting Friday, marching in the streets in uniform as anti-government protesters cheered them from the sidewalks.
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". Supporters chanted: "Police, you are not alone". "The police are joining their people", one officer said.
Police reports that joined the protests added pressure on Morales.
The mood was jubilant as tens of thousands of protesters filled the city's downtown throughout the night singing and setting off fireworks. He also called on supporters to join peaceful rallies.
Police from the Santa Cruz command also closed their station doors and several uniformed men climbed onto the roof, waving red, yellow and green Bolivian flags.
Morales, Latin America's longest-standing leader, won the election on October 20 but the vote count had been inexplicably halted for almost a day, sparking allegations of fraud and leading to protests, strikes and road blocks.
Opponents challenge an official count that showed Morales winning with 47% of the vote and a margin of just over 10 percentage points over his nearest competitor - enough to avoid the need for a runoff against a united opposition.
Carwil Bjork-James, an assistant professor at Vanderbilt University, said talk of a coup was premature.
"The government is now obliged to manage the crisis without the police and attempt to offer a solution that addresses the large share of Bolivians who have no confidence in the election outcome", he told the Observer. The opposition, which has alleged vote-rigging, says it will not accept the results because it was not consulted about the audit plan. "What the people are asking for is that their vote is respected", he said.
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