Correa, a US-educated economist, also renewed his pre-election promise to change the national constitution, calling the present arrangement "a perverse system that has destroyed our democracy, our economy and our society".
It was unclear what alternative system he was planning to put in place of Ecuador's existing multi-party democracy.
|Correa used Quichua, an|
Indian language [AFP]
His remarks drew applause from several left-wing leaders who were present.
Among them were Hugo Chavez, the Venezuelan president; Evo Morales, the Bolivian president; and Mahmoud Ahmadinejad, the Iranian president.
Other, less radical left-leaning leaders from Brazil, Chile, Peru and Nicaragua also attended the ceremony.
Correa said he would work to reduce poverty in Ecuador, adding that he aimed to reduce discrimination between the country's whites, descended from Spanish settlers, and the country's indigenous population.
Referring to Martin Luther King's dream of a world free of racial discrimination, Correa said: "My dream ... is to see a country without extreme poverty, without children begging in the streets, a nation without opulence but dignified and happy."
He closed his address with a message in Quichua, the language of Ecuador's highland Indians, saying: "A new day has arrived. This government belongs to all men and women. Let us not be frightened. God bless our land!"
After his swearing-in, Correa signed a document calling for a popular vote on March 18 to set up an assembly to change the constitution and accelerate his "citizens' revolution".
Correa has also said he will not agree to a free trade pact with the US, saying it would hurt Ecuador's farmers.
He has also said he will not extend the US military's use of the Manta air base on the Pacific coast for drug surveillance flights when a treaty expires in 2009.