London (CNN) -- Arguments over whether WikiLeaks editor-in-chief Julian Assange should be extradited to Sweden to face questioning on sexual misconduct allegations wrapped up Wednesday with no immediate answer.
Lord Justice Thomas and Justice Ouseley, the two appeals court judges who will make the decision, said they will consider both sides.
They set no date for a decision and did not change the terms of Assange's bail. He remains under house arrest.
Outside the court, supporters of Assange and Wikileaks held banners reading "Free Assange" and "Free Manning," a reference to U.S. Army Pfc. Bradley Manning, who is suspected of leaking classified information to WikiLeaks and is being held by the military pending a trial. The signs also said "Free Speech."
The case is not related to the work of Assange's website, which facilitates the publication of secret information. It made headlines last year for leaking documents and videos related to the wars in Iraq and Afghanistan, and thousands of U.S. diplomatic cables.
Assange's attorneys asked the appeals court to block his extradition to Sweden from the United Kingdom to face questioning on sexual misconduct allegations.
Lawyers for Assange told the court Tuesday that the European arrest warrant on which their client is being held was not a "fair and accurate description" of the facts of the case.
If the case had been accurately described, his lawyers said, the judges would see that the allegations did not constitute a crime under UK law.
Assange fought the case in London's High Court after a judge at Belmarsh Magistrates' Court ruled in February that the WikiLeaks head should be extradited.
At a news conference after the magistrate judge's extradition ruling on February 24, Assange lashed out at the decision to send him to Sweden.
He said to thrust someone into a foreign land where someone does not speak the language or understand the judicial system "is a very grave matter."
Assange has not been charged with a crime, but Swedish prosecutors want to question him in connection with sexual misconduct allegations related to separate incidents in August.
Assange denies the accusations, saying they are an attempt to smear him. His attorneys are fighting his extradition on procedural and human-rights grounds.
Judge Howard Riddell, however, dismissed almost all the arguments made by the defense when he made his decision in February. He ruled that the allegations against Assange are extraditable offenses.
Riddell rejected Assange's lawyers' argument that Swedish prosecutors did not have the authority to issue a European arrest warrant. He ruled that the warrant was valid.
Riddell also tossed out claims that Assange would not be able to obtain a fair trial in Sweden or that Swedish prosecutors had not made any effort to promptly interview Assange before he left Sweden last year.
"In fact this is untrue," the judge said in the ruling. He said Assange's Swedish lawyer had made a "deliberate attempt to mislead the court" and that it was Assange who had avoided interrogation before he left Sweden.
"It would be a reasonable assumption from the facts that Mr. Assange was deliberately avoiding interrogation before he left Sweden," Riddell wrote.
Assange's lawyers have raised the possibility that Sweden would hand him over to the United States if Britain extradites him to Sweden.
The prosecutor representing Sweden has dismissed that claim.
CNN's Atika Shubert, David Wilkinson and Andrew Carey contributed to this report.