NEW YORK (CNN) -- Chiquita Brands International faces a $7.86 billion lawsuit filed Wednesday on behalf of nearly 400 Colombian families who say the company should be held responsible for the "torture and murder" of their loved ones.

With a map of alleged victims, Jonathan Reiter makes his case Wednesday at a New York news conference.

Attorney Jonathan Reiter said his clients are seeking "damages for terrorism, war crimes ... and wrongful death."

The plaintiffs are asking for $10 million in compensatory damages and $10 million in punitive damages for each of the 393 victims named in the suit.

Earlier this year, Chiquita, as part of a plea agreement, admitted that what it called protection payments had been given to Autodefensas Unidas de Colombia, or AUC. AUC was named a terrorist organization by the United States in 2002, making it a crime to give them money.

The lawsuit alleges Chiquita's interaction with the paramilitary group went further than the payments -- it accuses the company of facilitating shipments of arms to the group.

"They conspired with the AUC, aided and abetted them in a far-reaching conspiracy and plan to control every aspect of banana growing, distribution and sale," Reiter said.

The attorney said one couple refused to sell their banana farm "for pennies" and were killed by AUC in 2001, and other murder victims had been directed to "sell their bananas only to Chiquita."

The families filing the suit will remain anonymous because of fear of reprisals in their home country, he said.

"The principle upon which this lawsuit is brought is that when you put money into the hands of terrorists, when you put guns into the hands of terrorists, then you are legally responsible for the atrocities, the murders and the tortures that those terrorists commit," Reiter said.

Responding to the allegations Wednesday afternoon, the company said, "Chiquita Brands International categorically denies the allegations made by these attorneys. We reiterate that Chiquita and its employees were victims and that the actions taken by the company were always motivated to protect the lives of our employees and their families."

Chiquita's director of communications, Michael Mitchell, went on to say, "Our company had been forced to make protection payments to safeguard our workforce. It is absolutely untrue for anyone to suggest that these payments were made for any other purpose."

Mitchell said the company will fight the allegations. "Chiquita has already been the victim of extortion in Colombia. We will not allow ourselves to become extortion victims in the United States."

In the March plea agreement, Chiquita Brands International agreed to pay a $25 million fine for the payments made by the company's former banana-producing subsidiary in Colombia.

During a government investigation, the company admitted to making payments to AUC even after outside counsel told the company those payments were illegal and should stop immediately. E-mail to a friend

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