An Arab-American civil rights organisation has asked "American Sniper" director Clint Eastwood and actor Bradley Cooper to denounce hateful language directed at US Arabs and Muslims after the release of the film about a Navy marksman.

The American-Arab Anti-Discrimination Committee (ADC) said in a letter to Eastwood and Cooper that its members had become targets of "violent threats" since early last week, before "American Sniper" went into general release. The letter said Eastwood and Cooper, the film's producer and star, could bolster the ADC's message of tolerance.

"It is our opinion that you could play a significant role in assisting us in alleviating the danger we are facing," said the letter, dated January 21. Reuters was provided a copy on Saturday.

The film is a box office hit and has been nominated for six Academy Awards, including best picture.

The ADC said it was working with the Federal Bureau of Investigation and police to assess the threats.

The film tells the story of Chris Kyle, a Navy SEAL sniper. His 160 kills in Iraq is considered the highest count in US military history. Some critics have said the film glorifies war and sanitises Kyle, who called Muslims "savages" in his memoir.

Kyle was killed by a disgruntled US veteran at a Texas gun range in 2013.

ADC President Samer Khalaf said on Saturday that it did not make sense to call for a boycott given the film's box office success.

"If we boycott it, it will only cause people to want to see it more," he said.

The Washington-based ADC asked Arabs and Muslims to send them copies of threatening messages they had received. More than 100 have been collected, all from social media.

"Nice to see a movie where the Arabs are portrayed for who they really are – vermin scum intent on destroying us," said one Twitter post collected by the ADC.

Jack Horner, a spokesman for Warner Bros., the studio releasing the film, said in a statement that the company, a unit of Time Warner Co, "denounces any violent, anti-Muslim rhetoric, including that which has been attributed to viewers" of the film.

He added, "Hate and bigotry have no place in the important dialogue that this picture has generated about the veteran experience."

Spokesmen for Eastwood and Cooper had no immediate response to requests for comment.