Foreign Minister David Choquehuanca denied that Snowden was on the plane, which landed in Vienna, and said France and Portugal would have to explain why they canceled authorization for the plane.
"We don't know who invented this lie. We want to denounce to the international community this injustice with the plane of President Evo Morales," Choquehuanca said from Vienna, where the plane landed.
Morales met with Russian President Vladimir Putin during a summit of major gas exporters in the Kremlin.
Morales said in an interview with Russia Today television that Bolivia would be willing to consider granting asylum to Snowden.
The rerouting of Morales' plane came as a string of countries appeared to offer Snowden little hope of getting him asylum.
Venezuelan President Nicolas Maduro told Russian reporters that his country has not received an application for asylum from Snowden and dodged the question of whether he would take Snowden with him when he left.
But Maduro also defended the former National Security Agency systems analyst who released sensitive documents on U.S. intelligence-gathering operations.
"He did not kill anyone and did not plant a bomb," Maduro said ahead of his meeting with Putin, the Interfax news agency reported. "What he did was tell a great truth in an effort to prevent wars. He deserves protection under international and humanitarian law."
Snowden, who recently turned 30, withdrew a bid for asylum in Russia when he learned the terms Moscow had set out, according to Putin's spokesman Dmitry Peskov. Putin said on Monday that Russia was ready to shelter Snowden as long as he stopped leaking U.S. secrets.
At the same time, Putin said he had no plans to turn over Snowden to the United States.
Snowden has applied for asylum in Venezuela, Bolivia and 18 other countries, according to WikiLeaks, a secret spilling website that has been advising him. Many European countries on the list - including Austria, Finland, Ireland, the Netherlands, Norway, Spain and Switzerland - said he would have to make his request on their soil.
WikiLeaks said requests have also been made to Brazil, China, Cuba, Ecuador, France, Iceland, India, Italy and Nicaragua.