“These men came to US courts because our laws, as they have for generations, allow their claims to be heard here.”
Burke said all four plaintiffs had been released from Abu Ghraib without charge.
One had been held in the jail for more than four years.
In a statement a spokeswoman for CACI International said the lawsuits repeated “baseless allegations” made more than four years ago in another case brought by the same lawyers.
“In the years that have passed since these claims first surfaced, nothing has changed to give any merit to unfounded and unsubstantiated claims,” the statement released to the Associated Press said.
It added: “These generic allegations of abuse, coupled with imaginary claims of conspiracy, remain unconnected to any CACI personnel.”
Allegations of abuse at the Baghdad prison first erupted in 2004 with the release of pictures of grinning US soldiers posing with detainees, some naked, being held on leashes or in painful and sexually humiliating positions.
The scandal eventually led to 11 US soldiers being convicted of breaking military laws, while five others were disciplined.
Neither US civilian nor military authorities have charged private contractors with crimes at Abu Ghraib.
The claimants’ lawyers say they are seeking unspecified payments high enough to compensate the detainees for their injuries, and to deter contractors from such conduct in the future.