Tanya Lokshina, who is a senior researcher in the office of Human Rights Watch in Moscow, told journalists after meeting with Snowden in the Sheremetyevo airport transit zone that she received the call before the meeting.
"They said: could you pass this along on behalf of the US ambassador (Michael McFaul) that the position of US authorities is... That he is not a rights activist, not a whistleblower... That he violated law and therefore has to be brought to justice," Lokshina said.
That the United States contacted Lokshina in this manner "further proves that the United States government's persecution of Mr Snowden and therefore that his right to seek and accept asylum should be upheld," said anti-secrecy group WikiLeaks in a statement.
Ambassador McFaul had refrained from making public comments about Snowden's extended layover in Moscow which has seen him marooned for nearly three weeks after the US authorities annulled his passport.
President Barack Obama last month however said that he is not going to have Snowden's case "suddenly being elevated to the point where I've got to start wheeling and dealing... So that he can face the justice system.