The men, mostly from Asian countries like India, Bangladesh and Sri Lanka, say they paid as much as $3,000 for transportation, a visa and the promise of a job. The money allegedly went to labor agents working for Najlaa International Catering Services, a Kuwaiti subcontractor to the U.S. company KBR.

In 2006, a U.S. Defense Department order barred this kind of labor exploitation. But the workers say it still goes on.

"About 95 percent of people paid money to agents, thousands of dollars in borrowed money. Their families depend on their income," Manoj Kodithuwakku, a 28-year-old from Sri Lanka who has been in Iraq for three months, told the Times.

Najlaa and KBR deny any wrongdoing and say the men are being paid or will be once they are cleared to work on U.S. bases.

"We work to very strict rules. We do not accept people being mistreated or mishandled," Marwan Rizk, the chief executive officer of Najlaa, said.