"If our two countries are to have a constructive relationship moving forward, Russian cooperation in this matter is essential,” Graham said.
The Republican senator's letter to the Russian ambassador follows a White House request of Russia to expel Snowden, the 29-year-old contractor who was the source of documents revealing classified phone and Internet surveillance programs by the NSA.
"We now understand Mr. Snowden is on Russian soil,” National Security Council spokeswoman Caitlin Hayden said in a statement.
“Given our intensified cooperation after the Boston marathon bombings and our history of working with Russia on law enforcement matters — including returning numerous high level criminals back to Russia at the request of the Russian government — we expect the Russian Government to look at all options available to expel Mr. Snowden back to the U.S. to face justice for the crimes with which he is charged.”
Snowden’s whereabouts were unknown on Monday morning, after he left Hong Kong to Moscow. He was allegedly supposed to take a flight from Moscow to Havana on Monday, but reporters on the plane said he was not on board.
WikiLeaks founder Julian Assange, whose group is aiding Snowden, said Monday that Snowden was “healthy and safe” but did not say where he was.
On Sunday, Graham said on "Fox News Sunday" that he thought there should be "consequences" if Russia or another country harbors Snowden.