"We need to be provided access to the entirety of the proceedings, which for four and half years has been in the hands of the Swedish prosecution and not in the hands of the defence," said Baltasar Garzon, a former Spanish judge who is Assange's lawyer.
Swedish prosecutors offered earlier this month to drop their previous demand that Assange come to Sweden for questioning about the 2010 allegations, making a significant U-turn in the case that has been deadlocked for nearly five years.
Sweden issued an arrest warrant for Assange, 43, in 2010 following allegations from two women in Sweden, one who claimed rape and another who alleged sexual assault.
The Australian former hacker, who has vehemently denied the accusations and insisted the sexual encounters were consensual, has been ensconced in Ecuador's embassy in London since 2012 to avoid extradition to Sweden.
He has long offered to be interviewed by prosecutors at the embassy or by video link.
"That offer has always been on the table. It has been repeated again, and again and again, and I am very pleased that the prosecution has finally accepted that offer," Assange said via video feed to a diplomatic conference on how to protect whistleblowers from prosecution.
He added however that "there are details to work through" since three countries were involved and in remained unclear which jurisdiction would apply.
TIMELINE: Julian Assange sex allegations
Garzon told AFP on the sidelines of the conference in Geneva that the defence team had yet to respond to the Swedish authorities' request for questioning to take place at the Ecuadorian embassy in London.
"Of course we will agree to the interrogation, but they have to guarantee minimum prerequisites," he said, stressing that giving the defence access to the investigation files was "simply the minimum rights of any person subjected to a judicial process".
Assange has refused to go to Sweden for questioning for fear he would be passed on to the United States, where investigations are going on against him and Wikileaks over the 2010 release of 500,000 secret military files on the wars in Afghanistan and Iraq and 250,000 diplomatic cables.
Garzon said Assange would remain in the Ecuadorian embassy until Britain grants him safe passage to Ecuador, where he has been granted asylum.
Swedish lead prosecutor Marianne Ny said in a press release earlier this month that the reason the request to interview Assange in London has now been made is that a number of the crimes he is suspected of will be subject to 'statute of limitation' in August 2015, which refers to the maximum time after an alleged offence that legal proceedings may be initiated according to Swedish law.
The statute of limitation for the most serious offence he is accused of, rape, runs out in 2020.