Protesters from police ranks rioted in angry reaction to austerity cuts in their pay and state benefits and held the president "hostage" for several hours at a hospital before loyal troops arrived to mount a timely rescue.
In the ensuing gunfire, casualties were reported but numbers weren't confirmed.
Correa said in a broadcast he went to the hospital for emergency treatment after he was hit by a tear-gas canister. Soon afterward, protesting police besieged the hospital and prevented him from leaving.
In an emotionally charged address to the protesters, Correa said: "If you want to kill the president, here he is. Kill him, if you want to. Kill him if you are brave enough.
"If you want to seize the barracks, if you want to leave citizens undefended, if you want to betray the mission of the police force, go ahead. But this government will do what has to be done. This president will not take a step back."
Although Correa has vowed to conduct a vigorous crackdown on police protesters, the incident capped a period of growing discontent over economic disparities and abuse of power and privilege by members of an elitist minority in the government.
The trouble started after the National Assembly passed a law Thursday that aims to introduce sharp cuts in government and state spending. Many state benefits due to be eliminated are seen by protesters as part of essential sustenance pay without which disparities will mount and hardship increase among government and state employees.
The greatest disparities are found among Ecuador's indigenous and Mestizo communities -- 90 percent of an estimated 14.7 million population -- and among black citizens, who comprise 3 percent of the total. The largest privileged groups are found in the 7 percent of the population that is of European origin.
Correa said the protests couldn't derail the government and urged the rioters to convey their demands through democratic means. However, many underprivileged groups say they aren't well represented in the National Assembly.
Correa rose to power in 2006 after a long period of military misrule. He also inherited massive economic problems, some caused by mismanagement, others by crashing oil and commodity prices. The El Nino impact on the economy from 1997 onward led to severe contraction of Ecuador's gross domestic product.
Correa said he would consider dissolving the National Assembly and ruling by decree until he could reassert his control on the government. However, he is likely to face opposition from within his government and in the Constitutional Court, which must approve such an option.
But he won instant support from the Union of South American Nations, which called an emergency session of heads of states in Buenos Aires. UNASUR officials said they would consider sending a high-powered delegation to Quito in expression of support to Correa.
Analysts said the unfolding crisis in Ecuador could demand more than cosmetic measures. Protesting security forces occupied several barracks and set up road blocks across the country, demanding the government abandon the austerity measures.
Despite signs there could have been a coup in the making, the military's timely support put Correa back in power though not fully in charge.
The police protest was part of wider discontent among government employees who say they work more hours for less pay than that available to private sector staff. They won support from the left wing of Correa's government that now wants the cuts deferred.
Ecuador lawmakers are nervous about adverse comparisons being drawn with Honduras, which went through a political turmoil after the country's highest court gave a green light to a coup that toppled elected President Jose Manuel Zelaya in June 2009. The reverberations from that action have prevented Honduras from returning to the international community despite a vigorous campaign.