More than 70 MPs have signed a letter urging the home secretary to ensure Julian Assange faces authorities in Sweden if they request his extradition.
He sought refuge in the Knightsbridge embassy in 2012 to avoid extradition to Sweden on sexual assault charges.
Aside from an alleged breach of bail - see a timeline of his case here - Assange was arrested in relation to an extradition request from the US.
Assange's lawyers meanwhile confirmed that USA prosecutors have 65 days to submit a full set of charges, raising the prospect of additional criminal allegations being introduced that would result in a far longer sentence.
"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.
Shadow Home Secretary Diane Abbott also faced criticism for appearing to down play allegations of rape and sexual assault against Mr Assange.
After getting the boot, Assange was taken to a London court where he was found guilty of failing to surrender.
Elisabeth Massi Fritz, the lawyer for the woman who reported being raped by Assange, told The Associated Press that she would "do everything" to have the Swedish case reopened so Assange can be extradited to Sweden and prosecuted.More news: Hazard shines for Chelsea
Labour leader Jeremy Corbyn has said Julian Assange should answer questions about sexual allegations.
But Ecuador withdrew his asylum status and allowed British police into the embassy on Thursday to arrest the white-bearded Assange.
The Department of Justice charged Assange with taking part in a computer hacking conspiracy, accusing him of scheming with Chelsea Manning, a former Army intelligence analyst, to break a password for a classified government computer.
The rape allegation has a limitation period which expires in August 2020, it adds.
According to the Home Office, the home secretary can bring a limited number of factors into consideration when deciding whether to order a person's extradition.
Assange's attorneys fear that in case of his handover to the U.S., he may face up to 35 years in jail or capital punishment.
Then she joked: "I do think it's a little ironic that he may be the only foreigner that this administration would welcome to the United States".
Previous comparable cases, involving accused hackers Lauri Love and Gary McKinnon, took between five and 10 years but eventually resulted in their extraditions to the U.S. being blocked.