On Sunday, the police commander, Gen. Yuri Calderón, instructed protesting officers to get back on the street and prevent attacks by thugs loyal to the president.
During an earlier nationally televised news conference, Morales said he would also replace members of the country's election board.
"In the following hours, in agreement with all political forces, [we] will establish [the steps] for this [to take place]", he said.
A radio station run by a farmers' union was also seized by protesters, Morales said.
Evo Morales was declared victor of the October election over his rival Carlos Mesa. He paved roads, sent Bolivia's first satellite to space and curbed inflation, according to AP. The country's constitutional court later ruled that term limits violated his human right to run for office, and the electoral court ultimately accepted his candidacy for a fourth term.
On Sunday, worldwide monitors called for the election result to be annulled, saying they found "clear manipulations" of the 20 October election results.
Videos released by supporters of President Morales' Movement for Socialism, which Governor Victor Hugo Vasquez belongs to, showed a group of people vandalizing and setting fire to his house on Saturday in Oruro department, Efe news reported.
After the October 20 vote, the country's first indigenous president declared himself the outright victor even before official results indicated he obtained just enough support to avoid a runoff with Mesa.
Whitney Houston's best friend confirms their love affair
Even while being pursued by Bobby Brown in 1989, Crawford writes, "She was more interested in Eddie Murphy , but he was elusive". Robyn explains Whitney told her they had to stop seeing each other, as she felt it would sink her music career.
The leader of a protest movement, Luis Fernando Camacho, said Morales "has fractured the constitutional order and must resign".
He called on Bolivians to protect their democracy and constitution.
So far, three people have died and hundreds have been injured in the unrest, which has lasted more than four weeks.
Bolivia's governing party has called on its supporters to defend President Evo Morales, after police in some cities joined protests against him. At a separate public event, Morales repeated he is not resigning.
As the fall-out from the audit report swept across Bolivia, there were signs that Morales' support was waning fast.
Morales' claim to have won a fourth term last month has plunged the country into the biggest crisis of the socialist leader's almost 14 years in power.
Mesa rejected the suggestion to hold talks.
Shortly before Morales announced his resignation, Bolivian TV channels aired footage of what they say was a presidential plane departing from El Alto International airport.