Assange's lawyer Jennifer Robinson comments came after the WikiLeaks founder on Monday said that he would soon leave the embassy as he is suffering from a heart condition and other ailments.
Robinson, in an ABC radio interview, said that the two-year stay in the embassy had had a "significant" impact on Assange's health.
"[He will leave] as soon as conditions can be negotiated that allow Julian to leave the embassy while his political asylum, to protect him from the risk of extradition to the US, [is] respected. And we haven't seen that happen yet," she said.
"He's been in there more than two years and the circumstances and the conditions inside the embassy aren't great," she said, adding there's nowhere for him to exercise and that's having significant impacts on his health.
"We have been asking that there be assurances given that he will not be extradited to the US, that is and has always been his main concern, and indeed is the reason for the grant of asylum that's seen him remain inside the embassy," Robinson said.
"It's very difficult to put a timeline to this."
Assange, 43, sought asylum at the embassy in June 2012 to avoid extradition to Sweden, where he faces allegations of rape and sexual molestation.
He fears extradition to Sweden could lead to him being transferred to the US to face trial over WikiLeaks' publication of classified US military and diplomatic documents.
"As Julian said, he'd like to be leaving the embassy soon, we'd all like to see that happen, but there are a complicated number of legal cases that are ongoing both in Sweden, and the ongoing grand jury investigation in the US which is reason for his asylum," Robinson said.
Robinson said she does not understand why a Swedish prosecutor is refusing to come to London to interview Assange so the case can proceed.
"Julian's remarks also last night refer to the fact that there's an ongoing appeal in Sweden that will be heard at the end of the European summer in which we're challenging his arrest warrant," she said.
She further said Assange had been refused permission to travel to hospital to seek treatment for his medical conditions.
"If he is required to leave the embassy for hospital treatment he would be arrested," she said, adding "This is a very serious situation and is the reason that this case has been taken up at the UN by more than 60 human rights groups around the world."
WikiLeaks founder Assange has heart, lung problem
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