WikiLeaks founder Julian Assange has "cooperated fully" with prosecutors questioning him over a Swedish rape allegation and hopes the case against him will now be dropped, his lawyer Jennifer Robinson says.

But she told reporters outside Assange's refuge at the Ecuadorean Embassy in London on Tuesday that even if Swedish authorities drop the case he will still have to stay inside the embassy while a US investigation into WikiLeaks' release of secret US government documents continues.

Assange on Tuesday finished two days of giving testimony on an allegation he raped a woman in Stockholm in 2010.

Swedish authorities had insisted he must return to Sweden to face the allegations but finally agreed to hear his evidence in the London embassy before an Ecuadorean prosecutor, with Swedish prosecutor Ingrid Isgren and a Swedish police investigator in attendance.

Isgren declined to comment to reporters as she left the embassy on Tuesday after the conclusion of Assange's testimony.

A statement on the Swedish Prosecution Authority's website said Ecuadorean authorities would provide a report on the Assange interview to Swedish prosecutors who will then "take a view on the continuation of the investigation".

The statement said that because the investigation was ongoing it was subject to confidentiality so details of the investigation could not be provided.

Robinson, an Australian human rights lawyer, told reporters that Assange has never been charged and he was cleared of the exact same allegation in 2010 by the chief prosecutor of Stockholm before the case was revived by the current chief prosecutor.

"This absurd politicised situation must come to an end," she said.

"Mr Assange is of course more optimistic now that the Swedish prosecutor has finally heard his side of the story and there's an opportunity now for this matter to be closed and we hope and expect that it will be".

But Robinson said even if the case was dropped Assange would have to remain inside the embassy while a US investigation in WikiLeaks' release of secret documents was ongoing and while the UK and Sweden refused to recognise his grant of political asylum by Ecuador.

"Our major concern is and has always been the risk of extradition to the United States and unless and until that investigation is closed he will remain inside the embassy," she said.

She said that the US investigation into Assange and WikiLeaks should be dropped under the First Amendment to the US Constitution, which relates to freedom of speech.

When asked about a request by Swedish investigators for a DNA sample from Assange, Robinson said he had already provided one in 2010.

It is not known how long Swedish prosecutors will take to decide on the Assange case.