Snowden filed the request with the Russian Migration Service on Wednesday, his lawyer Anatoly Kucherena said in comments quoted by Russian media.
The former National Security Agency (NSA) contractor received temporary asylum status in Russia after arriving in Moscow in June 2013. Snowden became stranded in the Russian capital last year on his way from Hong Kong to Cuba.
Snowden attempted to reach Cuba after disclosing a massive telecommunications and email surveillance program run by his former employer, the NSA, last year.
The United States subsequently revoked his passport and charged him with espionage and theft of government property.
His one-year asylum runs out on July 31, Kucherena said.
Russia's decision to grant him asylum has caused a diplomatic rift between Moscow and Washington.
hc/wr (AFP, AP, dpa)