The situation drew a stern rebuke from Brazilian President Dilma Rousseff, who said the incident was "life-threatening" for the Bolivian leader.
"The Brazilian government expresses its outrage and condemnation of the embarrassment imposed on President Evo Morales by some European countries," she said in a statement Wednesday. "The pretext that led to this unacceptable behavior -- the supposed presence of Edward Snowden in the plane of the president -- was fictional and a serious disrespect to the law and to international practices and standards of civilized coexistence among nations."
The impact of the European countries' actions extends far beyond Bolivia's borders, she said.
"The embarrassment to President Morales reaches not only Bolivia, but all of Latin America. It compromises the dialogue between the two continents and possible negotiations between them," she said. "It also requires prompt and explanation by the countries involved in this provocation."
The Union of South American Nations released a statement Wednesday saying the body "rejects categorically the dangerous act" of denying Morales' plane access. The leaders of the UNASUR countries are scheduled to meet on Thursday meeting in Cochabamba, Bolivia, to discuss the matter.
By Wednesday evening, the presidents of Argentina, Venezuela, Peru, Suriname, Ecuador and Bolivia had confirmed their plans to attend, said Ecuadorian Foreign Minister Ricardo Patino, who called the situation "very serious."
Cuba's Foreign Ministry also condemned the incident.
"This constitutes an unacceptable, unfounded and arbitrary act which offends all of Latin America and the Caribbean," the ministry said in a statement.
Argentina's President Cristina Fernandez de Kirchner described Morales' treatment in Europe as humiliating.
"This is not only a humiliation to a sister nation," she said during a military event Wednesday, "but to the whole South American continent."
So where is Snowden?
The situation is the latest twist in what has become a global guessing game over Snowden's next steps.
Snowden has admitted leaking classified documents about U.S. surveillance programs and faces espionage charges in the United States. He has applied for asylum in 21 countries, including Bolivia.
Morales, a left-leaning president who has long criticized the United States, had been attending a conference of gas-exporting countries in Russia, where he told the Russia Today news network that he would be willing to consider asylum for Snowden.
But Bolivian officials stressed that accusations that an official aircraft would harbor Snowden were baseless.
"We cannot lie to the international community by carrying ghost passengers," Choquehuanca said.
WikiLeaks founder Julian Assange urged Europe on Wednesday to demonstrate its willingness to defend freedom of information, whatever the fear of political pressure from its "best ally," the United States.
His comments came in a piece co-written with the secretary general of Reporters without Borders, Christophe Deloire, for French newspaper Le Monde.
European Union states should accord Snowden their warmest welcome, their article said. If he is abandoned in the international zone of Moscow's Sheremetyevo International Airport, it will mean European countries are "abandoning their principles and part of the reason for the EU," it said.
In recent days, a number of European nations have voiced concern about reports -- based on documents apparently provided by Snowden -- that the United States has been conducting surveillance on its European allies.
France believes it would be wise to delay U.S.-EU trade talks for two weeks in light of the allegations, French government spokeswoman Najat Vallaud-Belkacem said Wednesday.
She was echoing remarks made by President Francois Hollande this week after the claims first appeared in German and British media.
Germany's Economy Minister Philipp Roesler has said the reports of spying do influence the planned talks, said his spokesman, Adrian Toschev.
But the spokesman declined to back the French call for a delay to the talks, which are scheduled to begin Monday.