Ms Massi Fritz said in a text message sent to the Associated Press that "we are going to do everything" to have the Swedish case reopened "so Assange can be extradited to Sweden and prosecuted for rape".
If Sweden also makes an extradition request, it would be up to Britain's Home Secretary to determine which would take priority.
"We do not presume guilt, of course, but we believe due process should be followed and the complainant should see justice be done", it said.
Sweden suspended its investigation of serious sexual misconduct two years ago because Assange was beyond their reach while at the embassy.
After news broke that Assange had been arrested, the lawyer for the woman who accused him of rape tweeted that she and her client were shocked, but said they'd been hoping for it since 2012.
"A kneejerk response that presumes that hacking is acceptable if the perpetrators can claim that their motives were journalistic is particularly unsafe when it emanates from those aspiring to become prime minister or home secretary, such as Jeremy Corbyn and Diane Abbott".
The Daily Mail also picks up the tale, saying he faces decades in a United States jail after he was hauled out by eight policemen and put before a judge as extradition proceedings got under way.
Trump Administration Blocks Major League Baseball Deal For Cuban Players
Trump has especially stepped up pressure on Cuba recently over its support for Venezuela's socialist president, Nicolas Maduro. Last week, Cuba's baseball league said 34 players would be eligible to sign contracts directly with USA teams.
The official, who wished to remain anonymous, says United States authorities have already sent Britain a provisional arrest warrant regarding Assange's extradition.
It remains unclear whether Mr Assange used his own faeces, or someone else's, to allegedly smear on the walls of the embassy.
She said they had not received any prior notice of it and called on Swedish authorities to reopen the case.
A law change following the case of accused cyber-hacker Gary McKinnon, who has Asperger's, shifted responsibility away from ministers to the courts after then-home secretary Theresa May intervened to stop his extradition to the USA in 2012.
According to a criminal indictment that was only unsealed after the WikiLeaks founder's arrest, Assange is charged with conspiring with former army intelligence analyst Chelsea Manning to gain unauthorised access to a government computer. "We've ended the asylum of this spoiled brat", President Lenin Moreno said Thursday explaining his decision to withdraw protection of Assange.
After Assange's arrest, Swedish prosecutor Eva-Marie Persson was tapped to look into a request from a lawyer for one of the accusers, to find out whether the case can be pursued.
Assange denies the Swedish allegations, which have a limitation period that expires in August 2020.
Legal experts said on Friday that the case could take several years mired in British courts and, if appealed, potentially go all the way to the European Court of Justice.