The main concern expressed by Mr Assange and his supporters is that once extradited to Sweden, he would be in danger of being sent to the US, where he fears he could face the death penalty.
Many of Wikileaks' most prominent revelations came from massive releases of classified US military documents on the Afghan and Iraq wars, in July and October 2010. In April 2010, the site released footage showing US soldiers shooting dead 18 civilians from a helicopter in Iraq.
Despite the US not having made an extradition request, US Attorney General Eric Holder has previously said American officials were pursuing a "very serious criminal investigation" into the matter.
Mr Assange has also pointed to the case of Chelsea Manning, an ex American soldier formerly known as Private Bradley Manning, who was sentenced to 35 years in prison in the US for leaking classified material to Wikileaks.
However, legal experts have pointed out several obstacles any extradition and subsequent prosecution in the US would have to overcome.
Correspondents say that Sweden could apply a more stringent test than that used when an extradition is sought from the United Kingdom.
Also, even though the extradition would be according to Swedish law, the UK's approval would be needed.
Mr Assange's supporters have asked Sweden to guarantee that he would not be extradited to the US, which Swedish officials say they cannot legally do.
Swedish Foreign Minister Carl Bildt has however insisted that his country would not extradite a suspect to a country where they would face the death penalty.