WASHINGTON — 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."

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  • Russian President Vladimir Putin smiles as photographers try to make pictures of his dog Koney during his meeting with Jordan's King Abdullah II (not pictured) at Putin's residence in the Russian Black Sea resort of Sochi Aug.18, 2005. (Alexander Zemlianichenko, AFP / Getty Images)

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  • Russian President Vladimir Putin pets his dog Kuni as Germany's Federal Chancellor Angela Merkel looks on as they address journalists after their working meeting at the Bocharov Ruchei residence in Sochi Jan. 21, 2007. (Axel Schmidt, AFP / Getty Images)

  • Russian President Vladimir Putin plays with a dog as former US President George Bush look at him at the Bush family house at Walker's Point in Kennebunkport, Maine in July 1, 2007. Putin arrived in the United States for a "lobster summit" with Bush, aimed at defusing tensions which have spiked over irritants such as missile defense. (Mikhail Klimentyev, AFP / Getty Images)

  • Russian President Dmitry Medvedev and Prime Minister Vladimir Putin, accompanied by a dog, play badminton at the presidential residence in Sochi on Aug. 14, 2009. (Dmitry Astakhov, AFP / Getty Images)

  • Russian President Dmitry Medvedev and Prime Minister Vladimir Putin, accompanied by a dog, drive in an electric buggy at the presidential residence in Sochi on August 14, 2009. (Dmitry Astakhov, AFP / Getty Images)

  • Russian Prime Minister Vladimir Putin hugs a Bulgarian shepherd dog, a present from his Bulgarian counterpart Boyko Borisov after their press conference in Sofia on Nov. 13, 2010. (Nikolay Doychinov, AFP / Getty Images)

  • Russian Prime Minister Vladimir Putin plays with his Bulgarian shepherd dog named Buffy during their meeting at Putin's residence outside Moscow, the Novo-Ogaryovo, on Dec. 9, 2010. (Alexey Druzhnin, AFP / Getty Images)

  • Russian Prime Minister Vladimir Putin greets a soldier's dog as he visits a division of the Ministry of Internal Affairs in Balashiha, outside Moscow on July 22, 2011. (Alexey Druzhnin, AFP / Getty Images)