Anatoly Kucherena said after meeting Snowden in the Terminal E of the airport that the Federal Migration Service (FMS) had not yet granted the necessary certificate, Xinhua reported.
"The issue is not resolved. This situation is unique for Russia," he said.
Noting there had not been such cases or applications before, Kucherena said "Snowden has expressed his understanding of this".
Snowden would not contact media representatives in the near future for security reasons, he said.
"Of course, he intends to meet the press when the question of his status is finally clarified," the lawyer said.
Kucherena also did not rule out the possibility Snowden could receive approval for free movement in Russia "any time".
The most important thing for Snowden was to wait for the FMS's final decision, and he could appeal if the service rejected the application, he said.
The former CIA contractor is learning Russian, and could utter simple phrases during their talks, the lawyer said, adding that Snowden wanted to find a job here.
Kucherena said he had given Snowden some clothes and several Russian books, including the Fyodor Dostoevsky classic novel "Crime and Punishment".
He also told Snowden a number of Russian girls had a crush on him. The latter responded with laughter.