The letter, signed by mostly Labour MPs, urges Mr Javid to “stand with the victims of sexual violence” and ensure the rape claim against the 47-year-old can be “properly investigated”.
“We do not presume guilt, of course, but we believe due process should be followed and the complainant should see justice be done,” it says.
The rape allegation has a limitation period which expires in August 2020, it adds.
Inquiries into claims of molestation and unlawful coercion have already been timed out.
On Friday evening, shadow foreign secretary Emily Thornberry said Assange should be extradited to Sweden before any attempt to get him to the US.
She said she was “disgusted” the American allegation had been “allowed to eclipse” the sex offence case.
Extradition proceedings are dealt with by the courts.
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.
These include whether the person might be at risk of the death penalty or whether the requesting state might try to add additional charges it has not specified.
However, lawyer Rebecca Niblock said that, if Sweden made an extradition request, it would be for the home secretary to decide which would take precedence, considering factors such as which was made first and the seriousness of the offence.
The US Department of Justice has accused him of conspiring with former intelligence analyst Chelsea Manning to commit “one of the largest compromises of classified information in the history of the United States”.
Assange sought refuge in the Ecuador embassy, in Knightsbridge, west London, in 2012 to avoid extradition to Sweden over allegations of sexual assault. But after seven years, Ecuador abruptly withdrew its asylum and invited the police to arrest him on Thursday.
The MPs’ letter says both UK and US authorities seem to have been aware in advance of Ecuador’s decision to rescind Mr Assange’s political asylum.
“It is therefore of grave concern to us that it appears that the Swedish authorities were not aware of the plans made to arrest Mr Assange yesterday in London, and we would welcome clarity as to what action the UK authorities took to ensure that the Swedish prosecutors were informed in advance of this decision,” it adds.
After his dramatic arrest, Assange was taken to Westminster Magistrates’ Court and found guilty of a British charge of breaching bail. He spent Thursday night in custody and is facing up to 12 months in prison for that conviction.
Assange is due to face a hearing over his possible extradition to the US on 2 May.
Assange’s lawyer Jennifer Robinson said they would be fighting the extradition request. She said it set a “dangerous precedent” for journalists publishing information about the US.
The UN has called for his right to a fair trial to be respected during any extradition process.