A Russian lawyer for US National Security Agency leaker Edward Snowden has left the transit zone of Moscow's airport and entered Russia.

Anatoly Kucherena said Thursday that Snowden was issued papers that allowed him to leave Moscow's Sheremetyevo airport where he was stuck since his arrival from Hong Kong on June 23.

Snowden has received refugee status in Russia, WikiLeaks said.

"Edward Snowden has successfully acquired refugee status in Russia and will shortly leave the airport," the anti-secrecy organisation said on Twitter.