Previous demonstrations saw the seizure of two water treatment plants and oil installations, the burning of an armoured military vehicle and a crowd of protesters reaving storefronts and buildings in an area to the southwest of the capital.
"They want to turn Ecuador into Venezuela", Roldan said.
The demonstrators' main demand is the withdrawal of the fuel subsidy cut, which has sent transport and food prices soaring, though some were also urging Moreno to quit.
Correa faces multiple charges in Ecuador, including corruption and abuse of power.
The Ecuadorian government says some 700 people have been arrested so far in the protests. Moreno has received "firm backing" for his handling of the unrest from seven Latin American countries, including Brazil, Argentina and Peru, according to Peru's foreign ministry. Indigenous groups came forward to condemn the measures, believing that they would widen the country's economic gap.
From Belgium, where he lives, Correa has been applauding the demonstrators but scoffed at accusations of seeking a coup.
José Briones, secretary general of the president's office, said topics in an initial discussion with indigenous groups include aid for farmers, such as debt refinancing, irrigation and other technical assistance.More news: New Child and Adolescent Mental Health Center Opens
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"They are such liars ..." The energy ministry announced it was shutting down one of the country's two domestic oil pipelines, effectively suspending two-thirds of its distribution of crude, and protesters seized three oil facilities in the Amazon earlier this week. "They say I am so powerful that with an iPhone from Brussels I could lead the protests", he said, holding up his mobile.
"People couldn't take it anymore, that's the reality", he said, referring to the belt-tightening economic measures.
With protesters swarming around Quito, various government buildings were attacked overnight, authorities said, adding to looting and the destruction of ambulances and police vehicles in recent days.
State oil company Petroecuador warned that as many as 165,000 barrels of oil, or almost a third of total production, could be lost each day if the unrest continues.
"These incidents of vandalism and violence demonstrate there is some organized political intention to destabilize the government and break constitutional law, break democratic order", Moreno claimed during Monday's televised announcement. He also offered to free up resources for those hit hard by the rise in fuel prices.
Though he enjoys the support of business and the military, Moreno's popularity has sunk to under 30%, compared with 70% in 2017.
Thousands of indigenous people, some carrying long sticks, converged on Ecuador's capital Tuesday as anti-government protests and clashes led the president to move his besieged administration out of Quito.
Correa's office rejected the allegations in a statement, while Venezuelan opposition leader Juan Guaido, Maduro's USA -backed rival, threw his support behind Moreno, accusing Maduro for being responsible for the unrest.
He said his predecessor and former ally turned arch rival, Rafael Correa, and Venezuelan President Nicolas Maduro were behind the "destabilisation plan".