"To process the asylum application, (Snowden) must be in Ecuadoran territory," the president said in an interview with the private Oromar channel.
"At this moment, the solution of Snowden's destination is in the hands of Russian authorities."
Snowden, who faces espionage charges in the US over his revelations about a vast US surveillance program, has been in Moscow's international airport since arriving from Hong Kong last Sunday.
The ex-contractor for the National Security Agency, whose passport has been revoked, has requested asylum in Ecuador.
The president said his government would listen to opinions from US authorities, but that the final decision rested with Ecuador.
Earlier, Correa yesterday spoke with US Vice President Joe Biden on the topic, making many of the same points.
In his weekly address, Correa said Biden had asked Ecuador to reject the asylum request.
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