US President Barack Obama has denounced the leak as “deplorable” and various countries have tried to close down the site, sending it jumping from server to server in a bid to stay online.
At 2200 (East African Time) Monday, more than 598,633 people worldwide had signed the Avaaz petition.
Although the petition does not mention Assange, many supporters link the campaign against WikiLeaks to the allegations of sexual assault and rape made against the site’s founder in Sweden.
The 39-year-old Australian will appear in court in London for a second time Tuesday where his lawyers will make a second application for bail.
He was arrested in London on December 7 on an extradition warrant from Sweden, where prosecutors want to quiz him on the sexual assault claims.
He denies the allegations and his lawyers have said they are politically motivated.
Supporters are expected to gather outside City of Westminster Magistrates Court ahead of Assange’s expected appearance on Tuesday afternoon to protest his continued detention.
Last week, the judge denied him bail because he was a flight risk, but said he would like to see more evidence of the allegations.
The Stop The War Coalition, which is organising the protest, claims the US government and its allies have built up a campaign against Assange which culminated in his detention “on dubious charges”.
“We demand his immediate release, the dropping of all charges and an end to the censorship of WikiLeaks,” it says.
About 15 people protested outside the Swedish embassy in central London on Monday.
Organised by the Justice for Assange Campaign, they wore masks bearing Assange’s face and held up banners claiming he was a “political prisoner” and was being gagged.
Last week, Assange’s legal team said he had been moved into a segregation unit of Wandsworth prison in south London “for his own safety”.
Assange will be represented in court by high-profile human rights lawyer Geoffrey Robertson.