Updated

Two senators urged President Barack Obama on Friday to consider recommending a new site for the September international summit in St. Petersburg, Russia, if Moscow continues to allow National Security Agency leaker Edward Snowden to remain in the country.

Sens. Chuck Schumer, D-N.Y., and Lindsey Graham, R-S.C., introduced a resolution encouraging Russia to turn Snowden over to the United States, where he is accused of leaking information about U.S. surveillance programs. Snowden has applied for temporary asylum in Russia three weeks after arriving at a Moscow airport from Hong Kong.

The United States wants the former analyst sent home to face prosecution for espionage. The resolution is the latest congressional effort to increase pressure on Russia as it considers Snowden's request, reminding Moscow of the potential fallout.

The resolution said the president "should consider options, including recommending a different location for the September 2013 G20 summit in St. Petersburg, Russia, should the Russian Federation continue to allow shelter for Mr. Snowden."

Snowden's presence in Russia has roiled already rocky U.S.-Russia relations. The White House is considering canceling a fall meeting between Obama and Russian President Vladimir Putin in Moscow. While Obama could recommend another location for the summit, it is uncertain how many participating countries would back his move.

"On multiple fronts, Russia is becoming one of the bad actors in the world," Graham said in a statement. "Russia continues to provide cover to the Iranian nuclear program and sell sophisticated weapons to the (Bashar) Assad regime in Syria to butcher tens of thousands of its own citizens. For Russia to grant temporary asylum to Mr. Snowden on top of all this would do serious damage to our relationship."

Earlier this week, Graham suggested that the United States consider a boycott of the 2014 Winter Olympics in Sochi, Russia, in February if Russia grants asylum to Snowden.

Schumer said that "time and time again. President Putin is too eager to stick a finger in the eye of the United States — whether it is arming the murderous Assad regime in Syria, supporting Iran's nuclear development or now providing shelter and Russian state protection to Edward Snowden. Enough is enough."