Under the deal announced just before 10 p.m. Sunday, Moreno will withdraw the International Monetary Fund-backed package that included a sharp rise in the price of gasoline and diesel fuel.
Indigenous leaders, in turn, will call on their followers to end days of protests and street blockades.
The two sides say they will work together to develop a new package of measures to cut government spending, increase revenues and reduce Ecuador's unsustainable budget deficits and public debt.
The United Nations and Ecuadorian Bishops' Conference have announced that talks between indigenous protest leaders and Ecuador's government will begin at 3 p.m. local time (4 p.m. EDT) Sunday.
A statement from the U.N. office in Ecuador said officials from the organizations had been in contact with the two sides and that "we trust in the will of everyone to establish a dialogue in good faith and find a quick solution to the complex situation the country is living."
The announcement came after President Lenín Moreno ordered a 24-hour curfew and the army took to the streets in response to a day of attacks on government buildings and media offices.
The violence and military deployment closely followed the announcement of a possible softening of Ecuador's 10-day standoff. Indigenous leaders of the fuel price protests that have paralyzed Ecuador's economy said they were willing to negotiate with Moreno.
Ecuador's army took to the streets after President Lenín Moreno ordered the first 24-hour curfew in decades in response to a day of attacks on government buildings and media offices.
By Saturday night, soldiers had retaken control of the park and streets leading to the National Assembly and the national comptroller's office, which had been broken into by protesters who lit fires inside the building.
Moreno said the military would enforce the round the clock curfew in Quito and around critical infrastructure like power stations and hospitals in response to the day's violence. It was the first such action imposed since a series of coups in the 1960s and '70s.
"We are going to restore order in all of Ecuador," Moreno said.
Late Saturday night, Moreno announced some possible concessions in an economic package that was opposed by many Ecuadorians. But he didn't retract his decision to remove fuel subsidies, a step that triggered the nationwide protests and clashes.
Moreno said his government would address some concerns of protesters, studying ways to ensure resources reach rural areas and offering compensation for those who lost earnings because of the recent upheaval.