Speaking to the state-owned Rossiya 24 channel in footage broadcast Wednesday, Lon Snowden of Allentown, Pennsylvania, thanked the Kremlin for the "courage" shown in keeping his son safe.
Addressing his son, Lon Snowden said that "your family is well and we love you." He added that "I hope to see you soon, but most of all I want you to be safe."
The younger Snowden has been stuck in the transit zone of Moscow's Sheremetyevo airport since arriving from Hong Kong on June 23. Russia is considering his request for temporary asylum, which he submitted on July 16.
Putin has warned that Snowden could be granted asylum on condition he agrees not to hurt U.S. interests - implying that the American would have to stop leaking material on Washington's spying efforts.
Snowden's Russian lawyer, Anatoly Kucherena, has said the fugitive told him he could meet that demand.
The Guardian newspaper on Wednesday made a new report on U.S. intelligence-gathering based on information from Snowden, but Kucherena said the material was provided before Snowden promised to stop leaking.
"He warned me that he had already sent to the press an array of revealing information and secret documents and, unfortunately, could not stop its publication," Kucherena was quoted as saying by the Interfax news agency.
Snowden, who revealed details of a U.S. intelligence program to monitor Internet activity, has received offers of asylum from Venezuela, Nicaragua and Bolivia. However, the logistics of reaching any of those countries are complicated because his U.S. passport has been revoked.
Snowden would need the country he wants to reach to issue him travel documents and he would have to find a way to get there. The only direct commercial flight to the region, one that goes to Havana, Cuba, flies over Europe and the U.S., which could cause complications. Some European countries refused to allow Bolivian President Evo Morales to fly through their airspace on his way home from Moscow earlier this month due to suspicions Snowden was on his plane.
The elder Snowden said that, considering those issues, his son's best option may be to stay in Russia.
"If it were me, I would stay in Russia and that's what I hope my son will do," he said, adding that he hopes to be able to visit him in Moscow.
Kucherena told the Vesti-FM radio station on Wednesday that he is arranging for Snowden's father to visit Russia. Kucherena said that he would send Lon Snowden a letter of invitation to Russia later on Wednesday.
Kucherena said that Snowden asked him to get in touch with his father because "he needs moral support."
The elder Snowden told Russian television that he feels proud of his son. "My son is a principled young man, he is a man of courage and what he saw he couldn't live with," he said. "I know that I have raised him to do the right thing. Sometimes the right thing means personal sacrifice, and that's what he did."