On Friday, Swedish prosecutors said they were examining the rape case at the request of the alleged victim's lawyer.
The alleged victim's lawyer said she would do "everything we possibly can" to get the investigation reopened.
If found guilty of the US charges, Assange could get five years in prison.
The lawmakers also point out that several rape charges against Assange were dropped because their statute of limitations have expired and the only remaining charge will expire in August 2020.
Assange was arrested earlier Thursday at the Ecuadorian Embassy in London, and the US has charged him with conspiring with former Army intelligence analyst Chelsea Manning to break into a classified government computer at the Pentagon.
But Labour leader Jeremy Corbyn said Assange should not be extradited to the US.
Julian Assange "smeared poo on the walls" at the Ecuadorian embassy in London during his seven year stay there when he was claiming asylum, an Ecuadorian minister has claimed.
"We expect all the relevant authorities to ensure Mr Assange's right to a fair trial is upheld by authorities, including in any extradition proceedings that may take place", United Nations human rights spokeswoman Ravina Shamdasani told a Geneva news briefing.
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 U.S. in 2012.
Wikileaks co-founder Julian Assange could face a renewed investigation into an allegation of rape in Sweden.
James O'Brien revealed where he stands on whether or not the United Kingdom should extradite WikiLeaks founder Julian Assange to the USA to face charges of conspiracy to commit computer intrusion.
"Testimony usually weakens with time, and it's now been 10 years", he said, adding that, considering Assange is not "about to volunteer to come to Sweden", a new worldwide arrest warrant for him must be issued. He spent Thursday night in custody and is facing up to 12 months in prison for that conviction. She said it set a "dangerous precedent" for journalists publishing information about the US.
The US government's position with regard to these two individuals, as well as whistleblower Edward Snowden, is indicative of an illiberal attitude towards those demanding greater accountability and transparency of public institutions.
The UN has called for his right to a fair trial to be respected during any extradition process.