The 43-year-old Australian national, who looked pale and sported a beard, refused to elaborate on the timeframe as he addressed journalists alongside Ecuadorian Foreign Minister Ricardo Patino at the embassy in Knightsbridge, central London.
Assange said WikiLeaks' spokesperson Kristinn Hrafnsson had "said that he can confirm I am leaving the embassy soon".
Many reports have suggested that the anti-secrecy campaigner, reportedly battling heart defect and chronic lung condition, needs medical treatment for his ailments.
"There has been two years of great uncertainty and a lack of legal protection. This situation must come to an end. Two years is simply too long...We continue to offer him our protection," said Patino.
"It is time to free Julian Assange. It is time for his human rights to finally be respected," he added.
Patino is set to meet with British foreign secretary Philip Hammond in the next few weeks to discuss ways to resolve the situation.
But speaking after the press conference, Hrafnsson said Assange would only be able to leave the embassy when the UK government "calls off the siege".
Assange, whose website WikiLeaks published a huge tranche of secret US military and diplomatic documents that embarrassed the American government, has been living inside the Ecuadorian embassy building after he was granted asylum there in August 2012.
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