Journalists crowd near one of the entrances inside the terminal F of Moscow's Sheremetyevo airport, where Edward Snowden held a meeting with human rights NGOs. (Vasily MaximovAFP/Getty Images)

Former U.S. security contractor Edward Snowden left Moscow's international airport Thursday after Russia granted him temporary asylum, according to his lawyer Anatoly Kucherena.

Wikileaks was quick to tweet the news that Snowden had left with its own Sarah Harrison. The company has aided Snowden since his time in Hong Kong.

Some U.S. senators also jumped to Twitter to voice their disapproval of Russia's decision. Previously, the White House said the United States would be "deeply disappointed" if Snowden were allowed to leave the transit zone. Sens. John McCain (R-Ariz.) and Kelly Ayotte (R-N.H.), who have both been critical of the Obama administration's effort to "reset" relations with Russia, pointed to the asylum as evidence that the policy was not working.

Sen. Robert Menendez (D-N.J.), chairman of the Foreign Relations Committee, released a statement calling the action "a setback to U.S.-Russia relations."

Richard Haas, the president of the Council on Foreign Relations, also tweeted about the potential implications for the reset.

Russian President Vladimir Putin had previously suggested that Snowden could stay if he stopped leaking information damaging to the United States. Wednesday, The Guardian published documents, previously supplied by Snowden, exposing another secret NSA program for collecting data about users' Internet use.