Bolivian officials insisted Snowden was not on the plane, accusing France, Portugal and Spain Tuesday of bowing to U.S. pressure to rescind permission for Morales's plane to cross their airspace on a return trip to Bolivia, forcing it to land in Vienna to refuel, The New York Times reported.
Snowden is the fugitive former U.S. security contractor who revealed secret U.S. surveillance programs and fled from Hong Kong to Moscow to avoid extradition. The one-time National Security Agency contractor has been holed up in a transit zone in Moscow's Sheremetyevo International Airport.
The U.S. government filed charges against him, including two espionage-related ones.
On Monday, Morales, attending an energy conference in Moscow, was asked by Russian media if he would consider granting asylum to Snowden, who has been at Sheremetyevo Airport for more than a week, his passport revoked by the United States.
"Yes, why not?" Morales answered. "Of course, Bolivia is ready to take in people who denounce -- I don't know if this is espionage or monitoring. We are here."
However, he said, Bolivia had not received a request from Snowden, despite news reports indicating otherwise.
Morales' plane spent 13 hours on the tarmac at the Vienna airport, the facility's spokesman, Peter Kleemann, said.
Austrian media said the plane was headed to Bolivia, with a stopover planned in the Canary Islands. Bolivian officials said France and Portugal reversed their decisions and offered to allow the plane to fly through their airspace.
Austrian President Heinz Fischer said he visited Morales to "ensure that our procedures here in Vienna were all correct," the Times reported.
Morales characterized his unscheduled stop as "being held hostage."
Asked about Snowden's presence on his airplane, Morales did not comment directly, but said it would be impossible to bring a passenger who didn't have a valid passport.
"How could we have a person in our plane who has problems with his homeland? He has never sought asylum in Bolivia," Morales said. "We are very responsible in our actions and our respect for international conventions."
Austrian Interior Ministry spokesman Karl-Heinz Grundbock said Austrian border authorities performed a routine check of the passports of all on board after the plane landed and received permission to search the plane to ensure that Snowden was not aboard.
"The rumors were just that," Grundbock said.
Bolivian Defense Minister Ruben Saavedra, who was with Morales, accused the Obama administration of being behind the rumors, calling it "an attitude of sabotage and a plot by the government of the United States."
Upon hearing about France and Portugal initially refusing to let Morales' plane into their airspace, Latin American leaders voiced their ire.
Argentine President Cristina Kirchner said she spoke with Uruguayan President Jose Mujica who was "indignant" at the "humiliating situation," and she agreed.
"Mother of God! What a world!" she said.
Ecuadorean President Rafael Correa -- who also raised the possibility of asylum for Snowden -- railed on Twitter, calling the French and Portuguese actions an "affront to our America" and appealing to his fellow South American presidents to "take action."
Correa and Kirchner said they were trying to convene a meeting of the Union of South American Nations to discuss the matter.