Correa had to be rescued by the army from a hospital in the capital, Quito, after he was trapped there for several hours by disaffected police.
Two people died and dozens were injured in the unrest, officials told the BBC Friday.
The president and his supporters said the police revolt over a law cutting public employee benefits was an attempted coup. A state of emergency has been declared.
Correa said there would be "a deep cleansing of the national police" and that he would "not forgive nor forget" what had happened, the BBC reported.
The commander of the national police has resigned, a spokesman said Friday.
South American heads of state held an emergency meeting in Argentina and called for those behind the revolt to be tried and punished.
Members of the armed forces and police occupied several barracks, set up road blocks across the country, set tires on fire in the streets of Quito and other cities, and took over airports in Quito and Guayaquil, shutting them down Thursday, the BBC reported.
The president was being treated after inhaling tear gas fired by police who were protesting the austerity measures. He was smuggled out of the hospital in a wheelchair during the gun battle.
After his release, Correa, speaking from the balcony of the presidential palace, thanked a cheering crowd estimated in the thousands for their support and said he hoped the incident would be "an example to those who want to bring a change and stop the citizens' revolution without going through the polls."
Angry police said they were overworked and underpaid, CNN reported.
"We work 14 hours a day," a uniformed officer said on Ecuador TV. "We are the ones who never protest."
"Nobody has supported the police as much as this government, nobody has increased their salaries as much," Correa said after his release, CNN reported. "After all we've done for the police, they did this!"
Peru closed its border with Ecuador during the uprising and the U.S. State Department says it was "closely monitoring" the situation.
Correa said he was considering dissolving the National Assembly to rule by decree until new elections. Such a move would have to be approved by the Constitutional Court, the BBC said.