The state agency, which monitors human rights, identified the indigenous leader as Inocencio Tucumbi of Ecuador's Cotopaxi region.
The office of President Lenín Moreno, however, said the number of deaths was lower. It said two people had died in accidents linked to the violence across the country.
One person was hit and killed by a car, and another person suffered fatal injuries after a fall during protests in Quito, said José Briones, secretary general of the president's office.
There was no immediate explanation for the discrepancy in the reports on the death toll.
Also Thursday, indigenous demonstrators were holding captive at least eight police officers following anti-government protests.
The uniformed officers were brought onto a stage by protesters who are based at a cultural center in the capital, Quito.
One of the officers was forced to drape a national flag around his shoulders and don a hat of a style worn by some indigenous people.
Indigenous leader Jaime Vargas invited the captive police to join the anti-government campaign of the protesters.
Elsewhere in Quito, security forces patrolled after a day of protests that included clashes with police.
Ecuador's indigenous groups as well as labor organizations and other demonstrators mobilized after the removal of fuel subsidies, a step announced by Moreno last week.
The announcement led to a sharp increase in fuel prices and unrest in many parts of the country. The discontent widened to include calls for the resignation of Moreno, who has refused to quit.
Indigenous protesters played a major role in the 2005 resignation of Ecuador's president at the time, Lucio Gutiérrez, though the military's tacit approval was key to his removal.
Ecuador's cuts in fuel subsidies were among measures announced as part of a $4.2 billion funding plan with the International Monetary Fund, which said the package will strengthen the economy and generate jobs.
Indigenous groups condemn the deal with the IMF, saying austerity measures will deepen economic inequality.