The indigenous Indian leader, Antonio Vargas, says a rise in fuel prices is hurting the nation's poor.
The protestors, who are angry about government austerity measures, blocked main roads and set up camp at a university campus, promising they would not leave until they had achieved a peaceful takeover of the city.
The indigenous Indian leader, Antonio Vargas, says a rise in fuel prices is hurting the nation's poor.
Cuts in fuel subsidies and rising bus fares are part of economic reforms demanded by the International Monetary Fund (IMF).
The Indian protests come almost exactly a year after similar demonstrations in Quito brought down former President Jamil Mahuad.
No new coup
"We do not seek to topple this government," said Mr Vargas, president of the Confederation of Indigenous Nations of Ecuador.
But he said the government needed to change course.
"We will not back down until the government rescinds measures that are starving the Ecuadorean people," Mr Vargas said on Friday.
Ecuador is trying to implement radical economic reforms, including adopting the US dollar as the national currency.
IMF aid package
President Noboa has also introduced a three-year austerity plan in order to secure a $2bn aid package from the IMF.
The austerity measures have sent domestic heating oil prices up by 100% and gasoline prices up by 20% in the past two months.
The country's four million Indians - who make up about a third of the population - have been particularly hard hit by the measures.
The government has warned protesters it is prepared to employ whatever means are necessary to maintain law and order.