Kathryn Bigelow is firming up the cast for her high-profile film about the killing of Osama bin Laden as Republican politicians in the US continue to worry at claims that president Barack Obama's administration leaked details about May's special operations mission to the film-making team.

The Wrap reports that Bigelow has signed Joel Edgerton for a major role and is in talks with Jessica Chastain, Mark Strong and Edgar Ramirez. Previously announced members of what is shaping up to be a stellar cast include Tom Hardy, Idris Elba and Guy Pearce.

Bigelow, the Oscar-winning director of The Hurt Locker, had been planning a film about the hunt for Bin Laden long before last year's US Navy Seals raid on Bin Laden's compound in northern Pakistan. She and her screenwriting partner Mark Boal were therefore first out of the block in terms of bringing the story to the big screen, though other projects are now said to be under way with involvement from George Clooney and perennial historical controversialist Oliver Stone.

The still-untitled film is due out on 19 December, just after the US presidential election and has drawn flak from Republican politicians. New York congressman Peter King, chair of the house homeland security committee, has questioned how much information the Pentagon shared with Bigelow's team, and whether it was right to do so.

In a statement yesterday, CIA spokeswoman Jennifer Youngblood said: "CIA has been open that as part of our public outreach, the agency has over the years engaged with writers, documentary film-makers, movie and TV producers, and others in the entertainment industry."

The film's December release date will also see it positioned for a run at the 2013 Oscars, which will be held the following February or March. "With the death of Osama bin Laden, this film could not be more relevant. Kathryn and Mark have an outstanding perspective on the team that was hunting the most wanted man in the world," Sony Pictures' Amy Pascal said in a statement made after Bin Laden's death.

• This article was amended on 6 January 2012. The original stated that US presidential election would occur after the film's release on 19 December, when in fact the release will follow the election. This has been corrected.