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.
On Friday night crowds cheered dozens of police officers who marched down a main avenue and garrisoned themselves in the city's central police station. Police officers in other cities left the streets and returned to their stations, without explaining why.
The head of the national police said in a statement that forces around the country would fulfill their duties to ensure order and peace. Morales warned that Bolivia's democracy is at risk because of the coup d'etat attempt launched by violent groups that threaten the constitutional order, and denounced to the worldwide community 'this attack on the rule of law'.
In rapid succession 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 on Friday. His government issued a statement claiming that an opposition plot to oust the president was being led by Camacho and former President Carlos Mesa, who finished second in the October 20 election.
Bolivia has been rattled by protests, strikes and road blocks since the country held a presidential election on 20 October.
There was no immediate comment from either Camacho or Mesa.
Morales said he would also invite worldwide organizations including the Vatican, the United Nations and the Organization of American States (OAS), which is conducting an audit of the October vote. The opposition, which has alleged vote-rigging, says it will not accept the results because they were not consulted about the audit plan.
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.
Protests have been most intense in La Paz, Potosí and Santa Cruz, that latter an opposition stronghold where Camacho, president of the Pro Santa Cruz Civic Committee, is based. "We are asking that both sides hear us", Sergio Rengel, a leader in the tourism sector, told The Associated Press.
Morales' bid for re-election was controversial before it began.
'I call on our people to peacefully defend democracy and the Political Constitution of the State, in order to preserve peace and life as supreme assets above any political interest, ' the president posted on his Twitter account.
Morales, who took office in 2006, had previously refused to accept the results of a referendum upholding term limits for the president.