Assange's lawyers lodged an appeal on Wednesday to the Swedish Supreme Court to cancel an arrest warrant issued in 2010, after two women accused the WikiLeaks founder of rape and molestation.
Quashing the warrant would largely end the legal stand-off, which saw the Australian seek refuge in Ecuador's London embassy in 2012, to avoid arrest and likely extradition to Sweden. He did so after losing a legal battle in Britain against the extradition.
The 43-year-old refused to go to Sweden to refute the accusations, which he denies, as he fears Stockholm would extradite him to the US, where he is wanted over his part in WikiLeaks' publishing of classified military, diplomatic and intelligence documents.
Swedish prosecutors have refused to interview Assange in London, insisting he go to Stockholm to be questioned.
In November, a lower Swedish court rejected Assange's request that the extradition request be lifted, saying he should answer questions over the claims. But it did criticize prosecutors for failing "to examine alternative avenues" in the investigation.
Assange's lawyer hopes that taking the case higher in Sweden will end the impasse.
"We have to end this - the situation is completely stalled, and that's the point we raised in our appeal," said Assange's lawyer, Per Samuelsson.
"We are asking the court to give us access to the phone text messages that the two plaintiffs exchanged, and which (prosecutors) possess," Samuelsson said, saying he was certain the contents of the message would prove his client's innocence.
The complex in central London where Assange is exiled has been constantly guarded by police, at a cost reaching millions of pounds.
Last August, Assange told reporters he planned to leave the embassy "soon," without giving reasons for his announcement or disclosing where he would like to go.
jr/gsw (AFP, dpa)