Russian President Vladimir Putin had earlier stated that Moscow would grant him asylum if he stopped activities aimed at harming "our American partners."
Snowden agreed to Moscow's condition on Friday, according to Russian lawmaker Vyacheslav Nikonov, who took part in the Moscow meeting with the former CIA employee.
"He said he is aware of that condition and it would be easy for him to accept it. He is not going to harm the US because he is a patriot of his country," Nikonov told journalists after the gathering.
When asked whether Snowden had more revelations up his sleeve, Tatyana Lokshina of Human Rights Watch replied, "He says that his job is done."
Moscow could decide to grant political asylum to Snowden within two to three weeks, lawyer and Public Chamber member Anatoly Kucherena said.