Assange, 47, was dramatically arrested and dragged out of the Ecuadorian embassy in London yesterday, where he had been holed up for nearly seven years.
But she said Assange should face the criminal justice system if the Swedish government charged him.
U.S. prosecutors say Assange faces five years in prison if convicted of "conspiracy to commit computer intrusion", though further charges are expected to be brought against him.
"In the end, the then-home secretary, Theresa May, blocked his extradition on what she said were human rights grounds".
But WikiLeaks editor Kristinn Hrafnsson said he fears more charges will be added, meaning Assange could face decades in a United States prison.
WikiLeaks founder Julian Assange has exchanged a small room at the Ecuadorian Embassy in central London for a cell at Belmarsh Prison, a grim institution in the southeast part of the city where he nevertheless has certain advantages he didn't have when he was holed up, hiding from the law.
Swedish prosecutors dropped a rape investigation into Assange in 2017 because they were unable to formally notify him of the allegations - a necessary step in proceeding with the case - while he remained in the Ecuadorian embassy. According to the MPs letter, the Swedish victim's lawyer requested for the case to be reopened, but Stockholm authorities have yet to decide whether to satisfy the demand.
If found guilty of the USA charges, Assange could get five years in prison.More news: Blue Jackets vs. Lightning Game 2 Prediction: NHL Playoffs Betting Odds
More news: Like Dad, Like Daughter: Kim Kardashian Is Studying To Become A Lawyer
More news: Trivago actor arrested in Houston for DWI
However, legal experts have said the Government has very limited powers to block extradition even if there is the political will to do so.
Prosecutors in Sweden have since confirmed that, while the investigation has not been resumed, they are looking into the case.
"Julian Assange can not be extradited to Sweden when the European arrest warrant against him was withdrawn as early as May 2017".
It remains unclear whether Mr Assange used his own faeces, or someone else's, to allegedly smear on the walls of the embassy.
The MPs' letter says both United Kingdom and USA authorities seem to have been aware in advance of Ecuador's decision to rescind Mr Assange's political asylum.
The political debate over whether to extradite Assange is already taking shape, with Britain's opposition Labour Party urging the government not to hand him over to the Americans.
Pence denied that statements by President Donald Trump, in which he praised WikiLeaks during the 2016 USA election campaign, were in any way "an endorsement of an organization that we now understand was involved in disseminating classified information".