"Sweden must put pressure on Ecuador to get Assange handed over to Sweden," Elisabeth Massi Fritz, a lawyer for one of the two accusers, wrote in a statement.
"There has been much speculation in the media, much of it incorrect... This is not about any kind of conspiracy as some media outlets have claimed. My client is a plaintiff and a victim," she said.
The two women accused the Australian activist of rape and sexual assault in 2010, when he was in Stockholm on WikiLeaks business.
Assange has denied the accusations, arguing they are part of a smear campaign to discredit his whistleblower website.
He is wanted for questioning in Sweden, but has been holed up in the Ecuadorean embassy in London since June 2012 after he was granted asylum but denied free passage by British authorities out of the country.
Assange fears that if he is handed over to Sweden he will be passed onto the United States for his controversial diplomatic memo leaks. He claims he will face the death penalty in the US.
"I can say that Assange's claims about his extradition to the US, where he according to his own account would face the death penalty, is merely a way of circumventing the law in various countries to avoid taking responsibility for the acts he is currently suspected of committing," Massi Fritz wrote.
Sweden has repeatedly said it is waiting for Britain to act on the Swedish arrest warrant issued for Assange.
The government has insisted it will not interfere in the judicial process, and prosecutors have refused to question Assange outside of the Scandinavian country.
Assange's other accuser wrote in April about her ordeal on her blog, speaking out for what the Swedish media said was the first time.
The women's names have not been officially disclosed or published in the Swedish media but they have been circulated widely on the Internet as the Assange accusers.