The leftist leader already needled Washington last year by giving shelter to a Snowden ally, WikiLeaks founder Julian Assange, at Ecuador's embassy in London, protecting him from sexual assault claims in Sweden.
Now Correa, who was re-elected in February, is weighing Snowden's asylum request and said on Twitter on Monday that he would make the decision "that we deem to be the most appropriate, and fully respecting our sovereignty."
"This is an anti-imperialist posture that seeks to defend the capacity of small nations to take action in the international arena," said Michel Levi, a foreign policy expert at the Andina University of Quito.
Relations between the United States and Ecuador reached a low in April 2011, when Quito expelled US ambassador Heather Hodges after WikiLeaks released a diplomatic cable in which she suggested that Correa appointed a new police chief despite knowing he was corrupt.
A new US ambassador was installed last year.
In 2009, Correa ended an arrangement that allowed the United States to operate an anti-drug base on the Pacific coast.
The Snowden case could end any hope of the United States reviving trade benefits under a program that compensates Andean nations that help combat drug production, said Francisco Carrion, professor at the Latin American Social Sciences Faculty.
"There could be other repercussions in trade and investments, with requests for credit from the Inter-American Development Bank rejected by the United States, and a reduction in cooperation," Carrion said.
Snowden, who revealed a massive US surveillance program, was believed to be heading to Quito when he landed in Moscow, but he was not seen on a flight to Cuba on which he was booked on Monday and his whereabouts are a mystery.
Ecuadoran Foreign Minister Ricardo Patino, speaking during a visit to Vietnam, praised Snowden's actions, saying the 30-year-old fugitive was trying to "shed light and transparency" on US practices.
But Correa has himself been under fire from international rights groups over a new media law that critics say curtails press freedoms by cutting the private sector's share of radio and TV frequencies.
Marco Romero, director of global studies at Andina University, said the Snowden case puts Ecuador at the center of global debate on the limits of civil liberties when it comes to national security.
But he said Correa's position also serves "internal (political) consumption" because it contradicts of the criticism of his strained relations with the press.
Correa, who signed the controversial media law on Monday, accuses some news organizations of conspiring against him.
One day after Assange was given asylum last year, Ecuadoran journalist Emilio Palacio was granted asylum by the United States.
Palacio was sentenced to three years in prison and a huge fine for insulting Correa. But at the president's request, the court annulled the conviction, which also affected three directors of El Universo newspaper.