Activists have launched a campaign urging Hollywood heartthrob Brad Pitt not to make a movie based on what they call a biased account of Ecuador's battle with oil giant Chevron over environmental damage in the Amazon.

The campaign was launched after Pitt's production company, Plan B, bought the rights to a book called "Law of the Jungle" that chronicles the legal battle by the indigenous people of Ecuador's Lago Agrio region to win compensation for the mass dumping of oilfield waste between the 1970s and 1990s.

In 2011, an Ecuadoran court ordered Chevron to pay them $9.5 billion in damages, one of the largest environmental justice verdicts ever.

But a US court found last year that the plaintiffs' legal team, led by American lawyer Steven Donziger, conspired to win the case by "egregious fraud," including bribing a judge, writing the court's verdict themselves and secretly paying the authors of an ostensibly independent report.

"Law of the Jungle" delivers a harsh portrayal of the Ecuadoran justice system and of Donziger, a Harvard-trained lawyer whom author Paul Barrett wrote would "stop at nothing to win."

The new campaign, #BradDoTheRightThing, was launched by a group called Justice for Ecuador on the petition website change.org.

It said it was worried that a movie based on Barrett's book would "spread lies and misinformation about the destruction caused by Chevron-Texaco in Ecuador and undermine the efforts of the Ecuadorian people for justice."

The petition, which has gathered just over 2,000 signatures, appealed to Pitt and his wife Angelina Jolie to show their "recognized commitment to humanitarian causes" and sit on the rights to the book.

"We invite you to do nothing with those rights," it said.

"Do not produce a movie with this book but don't allow others the chance to do so either. We know you will do the right thing and make sure that these lies never make it to the big screen."

Chevron did not reply to AFP's requests for comment.

The petition comes a week after Ecuadoran President Rafael Correa invited Pitt to visit and see the environmental destruction allegedly perpetrated by Texaco, which Chevron bought in 2001.

He called for a global Twitter campaign showing the actor "how he is being used."