"Assange has grown noticeably thinner, and we are very concerned about his health," Ecuadorean Vice Foreign Minister Marco Albuja Martinez said during a visit to Moscow.
"If he falls ill we will have to choose between two alternatives: to treat Assange in the embassy or hospitalise him," Albuja Martinez said. "This is a very serious situation and it can affect Assange's human rights."
Assange, whose whistleblowing website angered the United States by releasing thousands of US diplomatic cables, was arrested in December 2010 on an extradition warrant from Sweden where he is wanted for questioning over allegations of rape and sexual assault made by two women.
He denies wrongdoing and says he fears that if he is extradited to Sweden he could be transferred to the United States where he could face criminal charges punishable by death.
The 41-year-old Australian broke the conditions of his bail when he entered the Ecuadorean embassy in London in June shortly after running out of legal options to avoid being sent to Sweden. He was later granted diplomatic asylum by Ecuador, remains at the embassy and would risk arrest if he leaves.
Ecuador has asked the British Foreign Office for a document that would enable Assange to enter hospital safely if necessary and return to the embassy with refugee status.
" Britain has not yet given assent to this request, but is considering its decision," Marco Albuja Martinez said.
Ecuador was pleased that Britain "did not reject it outright". "We will not put pressure on them and will patiently await an answer, so that Assange can receive medical treatment if necessary."