Michael Moore, Oliver Stone and Noam Chomsky are among signatories to letter delivered to Ecuador's embassy in London.
Other signatories included the author Naomi Wolf, comedian Bill Maher and Daniel Ellsberg, the former US military analyst turned whistleblower, who leaked the Pentagon Papers in 1971 and has been a long-standing supporter of Assange.
Robert Naiman, policy director at the Just Foreign Policy campaign group, delivered the letter to the embassy on Monday, along with a petition signed by more than four thousand Americans urging President Rafael Correa to approve Assange's request for asylum.
The letter, which has been posted online, states that its signatories believe Assange has good reason to fear extradition from the UK to Sweden, "as there is a strong likelihood that once in Sweden, he would be imprisoned, and then likely extradited to the United States".
Adding that the US government "has made clear its hostility to WikiLeaks", it says he could face the death penalty in the US if he was charged and found guilty under the Espionage Act.
"We also call on you to grant Mr Assange political asylum because the 'crime' that he has committed is that of practicing journalism," says the letter, which is addressed to Correa.
It concludes: "Because this is a clear case of an attack on press freedom and on the public's right to know important truths about US foreign policy, and because the threat to his health and well-being is serious, we urge you to grant Mr Assange political asylum."
Ecuador's ambassador to the UK, Anna Alban, has gone back to Ecuador to brief Correa on Assange's application and to hold a series of meetings at the foreign ministry.
Assange was set to be extradited to Sweden, where he faces accusations of raping a woman and sexually molesting and coercing another into sex in Stockholm in August 2010, while on a visit to give a lecture.
He denies all charges, saying the sex was consensual and the allegations against him are politically motivated.