The appeal by US Senators Charles Schumer and Lindsey Graham is part of a bipartisan resolution they introduced into the Senate to encourage Russia to hand over Snowden, with both lawmakers accusing Russian President Vladimir Putin of obstructionism in the standoff.
"It is past time we send a strong message to President Putin about Russia's actions and this resolution will help accomplish that goal,” Graham, a Republican from South Carolina, said in a statement.
Snowden, who faces prosecution in the United States for leaking highly sensitive classified data about the US National Security Agency's surveillance activities, submitted a request for temporary asylum in Russia on Tuesday, having been holed up at Moscow's Sheremetyevo Airport transit zone since arriving from Hong Kong on June 23.
The Senate resolution introduced by Schumer and Graham states that US-Russian ties are being damaged by Russia’s "continued willingness to provide shelter” to the fugitive and that Obama should "consider other options” to pressure the Kremlin, including recommending a new location for the G20 Summit, scheduled Sept. 5-6 in Putin’s hometown.
"Enough is enough. It’s time to send a crystal clear message to President Putin about Russia’s deplorable behavior, and this resolution will do just that,” Schumer, a Democrat from New York, said in the statement.
Both senators accused Moscow of supporting Iran’s nuclear ambitions and propping Syrian President Bashar Assad’s government in the civil war there, allegations that Russian officials have consistently rejected.
While Putin has said that Moscow will not extradite Snowden to the United States, where he could face the death penalty, the Kremlin has also tried to keep its distance from the case, emphasizing that it is a human rights issue.
Putin reiterated on Wednesday that Russia had warned Snowden not to "damage Russian-American relations,” saying they are more important than any intelligence scandal.
White House spokesman Jay Carney said Wednesday that Obama "intends to travel to Russia for the G20 summit,” but he wouldn’t say whether Obama would keep his scheduled meeting with Putin in Moscow when he travels to Russia.
The US senate resolution announced Friday comes just days after Graham said the United States should consider boycotting the 2014 Olympic Winter Games in Sochi if Russia grants asylum to Snowden.