Mr Assange, 41, was due to make his first public statement this afternoon, two months after he walked into the central London building seeking asylum.
Australian–born Mr Assange is facing extradition to Sweden.
Mr Assange remains at the centre of a diplomatic row involving six countries on five continents, having skipped bail to avoid extradition.
He is currently in the Ecuadorean embassy in London, which, under the terms of the Vienna Convention, British police cannot enter.
Mr Asaange, a former computer hacker, was granted political asylum by Ecuador after its ministers agreed he was facing persecution and the possible death penalty in the United States.
But he remains holed up in the embassy in Knightsbridge, surrounded by police who want to arrest him for breaching his bail conditions.
He is due to make a “live” statement at 2pm on Sunday but faces arrest if he leaves his haven to make his public comments.