"I feel a great deal of personal sympathy with Mr. Snowden," Assange told reporters in a conference call from Ecuador's embassy in London on the first anniversary of being holed up in the compound to avoid being sent to Sweden to face questioning in a sexual-offense investigation.
"We are in touch with Mr. Snowden's legal team and are involved in the process of brokering his asylum in Iceland," Assange said, adding WikiLeaks and Snowden's team were reviewing both the legal and practical obstacles of such asylum.
The Icelandic Embassy in Washington said Reykjavik was approached by Snowden advocates but would comment no further.
Icelandic Ambassador to China Kristin Arnadottir told Hong Kong's South China Morning Post an asylum applicant must already be in Iceland to be considered.
In an email she said Iceland's Interior Ministry handled all asylum applications.
The ministry had no immediate comment.
Asked if Snowden could fly to Iceland without being stopped by U.S. or allied officials, Assange said, "All those issues are being looked at by the people involved."
Snowden, a rogue former National Security Agency contractor, told British newspaper The Guardian, when he first leaked hundreds of classified documents on NSA surveillance, he wanted to seek asylum in a nation that shared his values. He said he thought Iceland was more aligned with his values than other countries.
He also expressed concerns about whether he would be safe there.
Snowden, 29, is believed hiding in Hong Kong. He has acknowledged he is likely to be prosecuted for the unauthorized disclosures.
U.S. officials have confirmed he is under investigation, but they have not charged him, at least publicly.
Assange, 41, declined to say if he had direct contact with Snowden. He also declined to say if Wikileaks was in touch with Snowden before he provided the phone and Internet surveillance details to The Guardian and The Washington Post.
"As a matter of policy, we do not discuss issues which may relate to sourcing," Assange said.
Assange also urged the Obama administration to drop its investigation into WikiLeaks.
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