Following tactics that have toppled previous governments, thousands of indigenous demonstrators have flooded the highland capital.

Some burst through security cordons to briefly enter the National Assembly on Tuesday, waving flags, pumping their fists and chanting: "We are the people!"

Elsewhere in Quito and other flashpoints, masked and stick-wielding protesters hurled stones and battled with security forces, who responded with tear gas. The clashes injured 19 civilians and 43 police officers, authorities said.

Facing the biggest challenge to his two-and-a-half-year rule, Moreno has refused to reinstate fuel subsidies he recently cut and ruled out stepping down.

"Under no circumstance," Moreno said in an interview with domestic TV channel Teleamazonas late on Tuesday. "I don't see why I should (resign) if I'm making the right decisions."

Moreno has declared a state of emergency and relocated government operations to the coastal city of Guayaquil where there has been less trouble.

In a written decree on Tuesday, Moreno ordered that authorities restrict movement close to government buildings and strategic installations between 8pm and 5 am to keep order.

The government is seeking mediation from the United Nations or Roman Catholic Church. 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.

Protests erupted last Thursday when the government cut fuel subsidies as part of a package of reforms, in keeping with a $US4.2 billion ($A6.2 billion) International Monetary Fund (IMF) loan.

Moreno told Teleamazonas the measures would help Ecuador rein in an "immense" fiscal deficit he inherited from leftist predecessor Rafael Correa, whom he accuses of misusing public funds and leaving behind a raft of unfinished or unneeded construction projects.

Australian Associated Press