Australia's Prime Minister, Scott Morrison, says Julian Assange is receiving the same level of consular support as any other Australian, adding there will be "no special treatment" for the WikiLeaks founder.
"He's not going to be given special treatment," Mr Morrison said on ABC television. "He'll get the same treatment and support as everyone else."
Mr Morrison said Mr Assange's matter concerns the US and not Australia.
"It has got nothing to do with us, it is a matter for the US, and there is a range of judicial matters.
"When Australians travel overseas and find themselves in difficulty with the law, they face the judicial systems of those countries."
Labor Senator Penny Wong said it was appropriate that Mr Assange receive consular support.
“There are legal proceedings underway in the UK," she told ABC Radio. "Obviously, there are matters there which will be dealt with by the appropriate legal processes," she said. “As an Australian citizen, he’s entitled to that consular support."
Assange will fight his extradition
Meanwhile, Mr Assange's lawyer Jennifer Robinson said the Australian government should do more to intervene in the case.
"It is time for the Australian government to step up and do what it should have done in 2010 when we asked them to do the first time, which is to reach out to the United States, our ally and ask this prosecution be closed.
"This is a matter of free speech. It is an Australian citizen who faces years, potentially decades or life in prison for having published material that the Walkley Awards gave him the most outstanding contribution to Australian journalism for."
She said the legal team will fight the extradition request "all the way", saying the move is a dangerous precedent and threat to free speech.
"This precedent if he is extradited means any media organisation, any journalist anywhere in the world, who publishes truthful information about the United States could face extradition and prosecution in the United States."
Arrested after seven years in Ecuador's London embassy
Mr Assange's seven-year hideout in Ecuador's London embassy ended on Thursday when British police dragged him out and arrested him on an extradition request from the United States to face hacking charges.
Footage shot by the Russian video news agency Ruptly showed Mr Assange - his worn face framed by a bushy white beard and shock of silver hair - being hustled out of the building by burly men in suits and pulled into a waiting police van.
The lightning-fast scene unfolded on an upmarket side street in the heart of London that has been Mr Assange's refuge from prosecution since 2012.
Police struggled to handcuff him but eventually lifted him out exactly an hour after they entered the embassy.
Ecuador cancels Assange's Ecuadorian citizenship
The moment of high drama came after Ecuador - increasingly frustrated with Mr Assange's stay under pro-US President Lenin Moreno - pulled its asylum and cancelled his citizenship after earlier curbing his access to the internet and mobile phone.
UK police said Mr Assange had been initially arrested for breaching his bail conditions in 2012 and then "further arrested on behalf of the United States authorities".
British Prime Minister Theresa May has welcomed the arrest of Mr Assange.
“This goes to show that in the United Kingdom no one is above the law,” Ms May said in parliament.
The behaviour of a narcissist: judge
The pony-tailed 47-year-old Australian gave a thumbs-up sign to the press gallery in court and opened up a copy of Gore Vidal's book "History of the National Security State" about the US military-industrial complex before his hearing began.
Judge Michael Snow pronounced Mr Assange guilty of the bail charge and remanded him in custody to face sentencing at an unspecified later date.
He faces up to a year in a UK prison and will have his US extradition case heard on 2 May.
In finding him guilty, judge Snow said Mr Assange's behaviour was “the behaviour of a narcissist who cannot get beyond his own selfish interest”.
"This is unlawful," Mr Assange yelled out at one point during the arrest, the court heard. "I am not leaving."

Julian Assange is taken away by Metropolitan Police. Source: Applied
Assange faces US charges of hacking conspiracy
Mr Assange had long suspected that he was secretly wanted by Washington for his decision to publish a trove of classified Pentagon documents detailing alleged US war crimes in Afghanistan and Iraq.
US authorities had steadfastly refused to confirm reports that they had issued a sealed indictment against Mr Assange - until Thursday.
The US Justice Department said Mr Assange was being charged with a computer hacking conspiracy relating to his work with former US intelligence analyst Chelsea Manning in March 2010.
"If convicted, he faces a maximum penalty of five years in prison," a US Justice Department statement said.
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Supporters of Julian Assange hold placards outside of the Ecuadorian Embassy in London earlier this month. Source: AAP
Guarantee against the death penalty
Mr Assange will now be at the heart of a legal and diplomatic tug of war pitting him and his legions of supporters - including Russian authorities - against the US justice system.
His links to Russia continued through the years of his confinement in the embassy.
Russia's state-backed RT channel aired 12 episodes of "The Julian Assange" show in 2012 in which he conducted video-link interviews with figures such as Hezbollah chief Hassan Nasrallah and US leftist thinker Noam Chomsky.
WikiLeaks also published damaging emails stolen from US presidential hopeful Hillary Clinton and her party's computer servers during her 2016 race against Trump.
US intelligence agencies believe the hack was conducted by Russia's military intelligence agency.
Mr Assange says he never knew the source of the politically-compromising material when he released it on WikiLeaks.
Mr Assange's supporters fear that his extradition will be followed by more serious US charges such as treason - a crime that carries the death penalty in wartime.
Ecuador's Moreno insisted that he had "asked Great Britain for the guarantee that Mr Assange will not be extradited to any country in which he could suffer torture or face the death penalty".
Debate on free speech re-ignited
Mr Assange's case has opened up a bigger debate about security and free speech.
His supporters view him as a fearless exposer of injustices such as torture and alleged war crimes committed by US forces - and then covered up.
Mr Assange's critics accuse him of cosying up to authoritarian leaders such as Russian President Vladimir Putin and putting Americans' lives at risk.
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The Wikileaks founder has been arrested for failing to surrender to the court. Source: AAP
The American Civil Liberties Union (ACLU) said: "any prosecution by the United States of Mr Assange for Wikileaks’ publishing operations would be unprecedented and unconstitutional".
The Reporters Without Borders (RSF) free speech group said Mr Assange's arrest "could set a dangerous precedent for journalists, whistleblowers, and other journalistic sources that the US may wish to pursue in the future".
Russian foreign ministry spokeswoman Maria Zakharova accused Britain of "strangling freedom" and fugitive US whistleblower Edward Snowden - himself hiding in Moscow since 2013 - said the arrest was a "dark moment".
Additional reporting: AFP.