Assange moved into Ecuador's embassy in London in 2012 to avoid arrest over now-dropped Swedish rape charges. He remains over fears he will be extradited to the United States and put on trial for WikiLeaks publishing leaked secret US military documents and diplomatic cables in 2010.
"No solution will be achieved without international cooperation and the cooperation of the United Kingdom, which has also shown interest in seeking a way out," she told foreign correspondents in Quito.
It is the first time Ecuador has proposed mediation to resolve the case.
Swedish prosecutors initially wanted Assange extradited to face the sexual assault allegations, but they dropped their investigation into him in May 2017. However, he still faces arrest by British police for violating the terms of his 2012 bail.
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