President Moreno has been pushing for further talks with the indigenous leaders but the rhetoric coming from the groups that took the police officers is uncompromising.
Anti-government protesters chant as the coffin that contain the remains of indigenous leader Inocencio Tucumbi, who protesters say died during the country's unrest, arrives to the Casa de Cultura where indigenous protesters ar.
Col. Cristian Rueda Ramos, one of several police officers who has been detained by anti-governments protesters, is made to hold an indigenous banner, don a national flag as a cape and a fedora-styled hat, while presented on.
The government's removal of fuel subsidies last week plunged Ecuador into upheaval, triggering protests, looting, vandalism, clashes with security forces, the blocking of highways and the suspension of parts of its vital oil industry.
Protests erupted in the nation of 17 million people last week when truck drivers took to the streets over fuel price rises. It was the first such action imposed since a series of coups in the 1960s and '70s.
"Under no circumstance (will I step down), and I don't see why I should have to if I am making the right decisions", said Moreno.
Vice President Otto Sonnenholzner told reporters that authorities have arrested a "significant number of foreign citizens" over the past week, many of whom confessed to having been paid between 40 and 50 dollars for participating in the riots that have forced the government into declaring a 60-day state of emergency, recently reduced to 30 days.
Moreno, 66, has accused his predecessor and one-time mentor Rafael Correa of fomenting the unrest. "What we saw today we haven't seen before".
Valencia said around two dozen foreigners, including Venezuelans, had been arrested.
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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 says the funds will strengthen the economy and generate jobs. Public transit fares have also gone up.
At least three private broadcasters complied, as indigenous and trade union leaders took it in turn to address the crowd.
They are evicted and Moreno orders an overnight curfew to protect public buildings. "They never do", she said.
More than 20 journalists inside the cultural center were barred for a while from leaving by protesters.
"It's ridiculous", Correa said. Describing himself as a victim of "political persecution", he said he has been charged with a total of 29 offenses.
Mr Moreno's government lifted the petrol and diesel subsidies last Tuesday as part of a $4.2billion (£3.4bn) loan deal with the International Monetary Fund reached previous year that hinges on belt-tightening reforms. Panic and speculation sent prices soaring, with costs of some products doubling or more.
Ecuador's indigenous people, wracked by poverty and underserved by government programs, were infuriated. Over the last week, thousands of streamed into Quito from the Amazon rainforest and the Ecuadorian Andes.
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.