The US may be about to press charges against Julian Assange, the editor-in-chief of WikiLeaks, one of his lawyers said today.

Jennifer Robinson said an indictment of her client under the US's Espionage Act was imminent. She said her team had heard from "several different US lawyers rumours that an indictment was on its way or had happened already, but we don't know".

According to some reports, Washington is seeking to prosecute Assange under the 1917 act, which was used unsuccessfully to try to gag the New York Times when it published the Pentagon Papers in the 1970s.

Robinson said Assange's team did not believe the US had grounds to prosecute him but understood that Washington was "looking closely at other charges, such as computer charges, so we have one eye on it".

Assange is in Wandsworth prison in south London after being refused bail on Tuesday. Sweden is seeking his extradition over allegations of sexual assault.

Speaking to ABC News, Robinson said she did not believe the Espionage Act applied to Assange, adding: "In any event he's entitled to first amendment protection as publisher of WikiLeaks and any prosecution under the Espionage Act would in my view be unconstitutional and puts at risk all media organisations in the US."

Robinson said Assange was being held in solitary confinement in London with restricted access to a phone and his lawyers.

"This means he is under significant surveillance but also means he has more restrictive conditions than other prisoners. Considering the circumstances he was incredibly positive and upbeat."

Earlier this week, the US attorney general, Eric Holder, said the United States had been put at risk by the flood of confidential diplomatic documents released by WikiLeaks and he authorised a criminal investigation.

Holder said: "The lives of people who work for the American people has been put at risk; the American people themselves have been put at risk by these actions that are, I believe, arrogant, misguided and ultimately not helpful in any way. We are doing everything that we can.

"We have a very serious, active, ongoing investigation that is criminal in nature. I authorised just last week a number of things to be done so that we can hopefully get to the bottom of this and hold people accountable, as they should be."

In a letter to the Guardian today, prominent supporters including John Pilger, Terry Jones, Miriam Margolyes and AL Kennedy called for Assange's release. "We protest at the attacks on WikiLeaks and, in particular, on Julian Assange ," they wrote, adding that the leaks have "assisted democracy in revealing the real views of our governments over a range of issues".