Putin: Snowden warned over actions
Snowden has applied for temporary asylum in Russia, three weeks after arriving at one of Moscow's international airports from Hong Kong. The United States wants him sent home to face prosecution for espionage.
Granting Snowden asylum would add new tensions to US-Russian relations already strained by criticism of Russia's pressure on opposition groups, Moscow's suspicion of US missile-defence plans and Russia's resistance to sanctions against the regime of Syrian president Bashar Assad.
On a visit to the Siberian city of Chita, Mr Putin said "we have warned Mr Snowden that any actions by him connected with harming Russian-American relations are unacceptable," according to Russian news agencies.
Snowden could finally leave the transit zone of Sheremetyevo airport after Russian authorities review his asylum request, his lawyer said later.
Anatoly Kucherena told the news agency Interfax he believes Moscow could decide within a week whether to grant Snowden asylum.
"The question of giving him temporary asylum won't take more than a week. I think that in the near future he will have the possibility to leave the Sheremetyevo transit zone," Mr Kucherena said.
How long the asylum process could take for Snowden is unclear. Russia's Federal Migration Service is required to consider the application within three months, but could do it faster.
Snowden is believed to have spent his time since arriving in Moscow in the Sheremetyevo airport transit zone, which is technically not Russian territory.