In office since 2007, Correa has drawn increasing criticism over a constitutional reform package that would allow him to stand for reelection when his current term ends in 2017.
Discontent has been amplified by an economic slowdown gripping the South American oil producer, hit hard by sliding crude prices.
Indigenous protesters, who have been particularly vocal critics of Correa, blocked roads in six of Ecuador's 24 provinces yesterday, including the Pan-American Highway to Peru, officials said.
"We don't want indefinite reelection because we're going to end up in a dictatorship," he told journalists.
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But -in a setback for protesters- transport, education and health services were all operating normally in the country's largest cities despite a call for a general strike.
In a fiery speech to supporters Correa called the protests a failure.
"Today everyone possible came together, and they have not managed to achieve anything, they have failed and continue to fail because they lack popular support, legality and legitimacy," Correa said, warning that he will not be subject to "blackmail."
A heavy police presence was on the streets in key cities, including 5,000 officers in Quito.
Pro-government demonstrators were gathered outside the presidential offices in the capital to block what Correa has warned could turn into a coup attempt.
"We don't want coup plotters to keep tearing things down," said pro-government rural leader Carlos Litardo.
At the end of the day Thursday, police clashed with anti-government demonstrators outside the presidential offices in Quito, firing tear gas and making arrests.
Correa, who has faced repeated protests since June 8, recently admitted they were a "tough test" for his administration.