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Julian Assange's wife Stella Moris says there been a "shift" in the federal government's approach to her husband's case following Labor's election win.
UK Home Secretary Priti Patel approved the extradition of Mr Assange to the US at the weekend.
The Wikileak founder's legal team has 14 days to lodge an appeal in the UK High Court.
Ms Moris, a human rights lawyer, said she was "feeling a shift".
"It feels like we've been running a marathon for a long time, and you know, that's hard, mentally and physically," she told ABC radio on Monday.
"But now it feels like we have many people running alongside us and at the finish line."
Ms Moris said she had been "preparing for the worst" and was worried for Mr Assange's life while being held in Belmarsh prison.
Speaking from Melbourne, Prime Minister Anthony Albanese stood by comments he made late last year, where he said he didn't see the purpose of the "ongoing pursuit" of Mr Assange.
However, he said the government would deal with the matter through diplomatic channels.
"There are some people who think that if you put things in capital letters on Twitter and put an exclamation mark, then that somehow makes it more important," he told reporters.
"It doesn't. I intend to lead a government that engages diplomatically and appropriately with our partners."
Immigration Minister Andrew Giles said Mr Assange's case had been taken "very seriously" and consular support will continue to be provided.
"It was last year that Anthony Albanese ... made clear that enough was enough for Julian Assange and the treatment that he had been subjected to," he told ABC radio on Monday.
"That was true, then it's even more true now."
Mr Giles said there was no better person to be advocating for Mr Assange than Foreign Minister Penny Wong.
Greens leader Adam Bandt said he was concerned the Albanese government was "soft pedalling" on working to bring Mr Assange back to Australia.
"I'm very much hopeful that the government will act on the noises that they made in opposition and do what they've said that they would do, which is take advantage of the special relationship that we supposedly have with the United States and of course with the United Kingdom as well," he told ABC radio.