Officials in both Austria and Bolivia said Edward Snowden was not on the plane.
France and Portugal reportedly refused to allow the Moscow-Bolivia flight to cross their airspace.
Edward Snowden is reportedly seeking asylum in Bolivia and 20 other countries to avoid extradition to the US.
Bolivian Foreign Minister David Choquehuanca told reporters on Tuesday that France and Portugal had closed their airspace over the “huge lie” that Edward Snowden, 30, was on board.
“We don’t know who invented this lie, but we want to denounce to the international community this injustice with the plane of President Evo Morales,” he said.
Austrian foreign ministry spokesman Alexander Schallenberg said Edward Snowden was not on board the Bolivian leader’s aircraft.
The Bolivian defense minister, also on the flight, pilloried the US after the unscheduled landing.
“This is a hostile act by the United States state department which has used various European governments,” Ruben Saavedra said.
The Falcon aircraft was reportedly allowed to refuel in Spain before the jet went on to Vienna. President Evo Morales was said to be at the airport in Vienna discussing his return route to Bolivia early on Wednesday.
French officials said they could not confirm whether they had denied permission for President Evo Morales’ plane to fly over their territory. Portuguese officials could not immediately be reached for comment.
The Bolivian president had been on a visit to Moscow, where Edward Snowden, a former CIA contractor, has reportedly been holed up in an airport transit area since arriving from Hong Kong on June 23.
President Evo Morales told Russian television that Bolivia had not yet received an application from Edward Snowden, however, his request, if sent, would be considered.
“Bolivia is ready to accept people who disclose espionage if one can call it this way,” he said.
President Evo Morales and Venezuelan President Nicolas Maduro had been in Moscow for a meeting of gas-exporting countries.
Nicolas Maduro said he had not formally received an asylum request, but expressed support for Edward Snowden, saying he “deserves the world’s protection” from the United States.
“Why are they persecuting him? What has he done? Did he launch a missile and kill someone? Did he rig a bomb and kill someone? No. He is preventing war,” he told Reuters news agency.
Edward Snowden withdrew his application to Russia after President Vladimir Putin said he could stay only on condition that he stopped damaging Russia’s “American partners” with his leaks, Kremlin spokesman Dmitry Peskov said.
He is wanted by the US on charges of leaking secrets he gathered while working as a contractor for the National Security Agency (NSA), America’s electronic spying agency.
On Tuesday, National Intelligence Director James Clapper apologized for telling Congress in March that the NSA did not have a policy of gathering data on millions of Americans.
He said in a letter to Dianne Feinstein, head of the Senate intelligence committee, that his answer had been “clearly erroneous”.
The leaking of thousands of classified intelligence documents prompted revelations that the US has been systematically seizing vast amounts of phone and web data.
WikiLeaks, which says it is advising Edward Snowden, said most of his asylum requests had been handed to the Russian consulate at Moscow’s Sheremetyevo airport late on Sunday for delivery to the relevant embassies in the capital.
Edward Snowden asylum requests:
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