Morales again blamed Washington for pressuring European countries to refuse to allow his plane to fly through their airspace on Tuesday, forcing it to land in Vienna, Austria, in what he called a violation of international law.
He had been returning from a summit in Russia during which he had suggested he would be willing to consider a request from Snowden for asylum.
In a joint statement after the summit, the presidents demanded an explanation and an apology from France, Italy, Portugal and Spain. They also said they would back Bolivia's official complaint with the UN Human Rights Commission.
Latin American leaders were outraged by the incident, calling it a violation of national sovereignty and a slap in the face for a region that has suffered through humiliations by Europe and several US-backed military coups.
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"We do not need the embassy of the United States."
Morales' government has had a conflictive relationship with Washington. It expelled the US ambassador and agents of the US Drug Enforcement Administration in 2008 for allegedly inciting the opposition.
The Andean nation restored full diplomatic ties with the US in 2011. But relations soured again amid mutual distrust on drug war politics and hit an especially low point after Secretary of State John Kerry referred to Latin America as Washington's "backyard" in April 2013.
"We're not going to accept that in the 21st century there's first, second and third rate countries," Correa said.
"The leaders and authorities in Europe have to take a lesson in history and understand that we're not 500 years behind. This Latin America of the 21st century is independent, dignified and sovereign."
Venezuelan President Nicolas Maduro protested alleged attempts by Spanish officials to search the Bolivian presidential plane. Argentine President Cristina Fernandez demanded an apology for the plane ordeal.