White House spokesman Jay Carney said that such a move was not consistent with Moscow's assurances that it did not want the Snowden affair to harm US-Russia relations.
"Providing a propaganda platform for Mr Snowden runs counter to the Russian government's previous declarations of Russia's neutrality," Carney said.
"It's also incompatible with Russian assurances that they do not want Mr Snowden to further damage US interests."
Carney also renewed a US call on Russia to expel Snowden so that he could be returned to American soil to face trial for leaking US national security secrets.
Snowden earlier told activists he wanted to claim asylum in Russia until he can travel on to Latin America, in his first encounter with the outside world since becoming marooned at a Moscow airport three weeks ago.