PARIS (Reuters) - Human rights groups have filed a lawsuit in France alleging that former U.S. defense secretary Donald Rumsfeld allowed torture at U.S.-run detention centers in Iraq and Guantanamo Bay in Cuba.

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The plaintiffs, which include the French-based International Federation of Human Rights Leagues (FIDH) and the U.S. Center for Constitutional Rights (CCR), say Rumsfeld authorized interrogation techniques that led to rights abuses.

The United States says it does not torture, though it has authorized several methods widely condemned by rights groups such as exposure to extreme temperatures and ‘waterboarding’, or simulated drowning.

“We will only stop once the American authorities involved in the torture program are brought to justice,” CCR chief Michael Ratner said in a statement posted on the FIDH Web site.

“Donald Rumsfeld must understand that he has nowhere to hide. A torturer is an enemy of humanity,” he added.

The plaintiffs argue in their filing, which was also posted on the FIDH Web site, that French courts have universal jurisdiction -- allowing them to try foreigners in cases that occurred abroad -- under the 1984 Convention Against Torture.

They said Rumsfeld was visiting France on Friday and called for him to be detained.

“Rumsfeld’s presence on French territory gives the French courts the authority to try him, in that he ordered and authorized torture and other inhuman and degrading treatment on detainees at Guantanamo, Abu Ghraib and elsewhere,” the FIDH said in its statement.

The Abu Ghraib jail in Iraq hit the headlines in April 2004 when details of the physical abuse and sexual humiliation of Iraqi prisoners by U.S. soldiers were made public, badly damaging the reputation of the U.S. military.

Former prisoners at Guantanamo Bay are suing Rumsfeld and 10 military commanders for alleged torture and violations of their religious rights during their detention there.

The CCR and FIDH have already filed suits in Germany in 2004 and 2006 in a bid to have Rumsfeld tried for rights abuses.

Both were rejected by the courts, though an appeal is due to be heard in the second case next week, the groups said.

The German-based European Center for Constitutional and Human Rights was also a party to the French case.