The 30-year-old NSA leaker and now espionage suspect was supposed to board a flight from Moscow to Havana, Cuba, but Snowden did not board the flight, ABC News learned. Snowden's seat on the Aeroflot plane was empty, even though Snowden checked in twice - once on the phone and once on his computer.
Though Snowden's exact location remains unknown, he is "in a safe place," according to WikiLeaks founder Julian Assange.
Assange, who has been holed up in the Ecuadorian embassy in London since he was granted asylum there last summer, told reporters that Snowden is travelling with a WikiLeaks representative, and that both are "healthy and safe" and in contact with their legal team. He declined to say anything further about where Snowden is, but did say that Snowden's spirits are high.
Snowden has not been seen or publicly photographed since his apparent arrival in Moscow on Sunday. Snowden's apparent plan was to fly to Cuba and then make his way to Ecuador to seek political asylum. Snowden had also previously discussed seeking asylum in Iceland.
U.S. officials thought they boxed in Snowden in Hong Kong, but officials in China said the arrest request from Washington was flawed and Snowden was allowed to leave the country on Sunday, making his way to Russia.
The U.S. State Department has warned countries to send Snowden back to the U.S., but so far he has not been stopped.
He has with him four laptops with the U.S. government's most sensitive secrets.
The White House said it expected the Russian government to send Snowden back to the United States, but President Vladmir Putin's secretary denied any knowledge of Snowden's movements.
"What's infuriating here is Prime Minister Putin of Russia, aiding and abetting Snowden's escape," said Sen. Chuck Schumer, D-New York. "The bottom line is very simple: Allies are supposed to treat each other in decent ways, and Putin always seem almost eager to put a finger in the eye of the United States."
U.S. Secretary of State John Kerry has said that it would be deeply troubling if Russia and China had prior notice of the whistle blower's travel plans and allowed him to leave their countries.
Kerry defended the U.S. surveillance program and called Snowden a traitor.
"We don't know specifically where he may head or what his intended destination may be," said Kerry. "He places himself above the law, having betrayed his country, with respect to the violation of his oath, and I think there are very serious implications in that."
ABC News and the Associated Press contributed to this report.