Gross was tried in a Cuban court on charges of crimes against the state and sentenced to 15 years in prison in 2011. In previously released testimony from the trial, Gross called himself a "trusting fool."
"I was duped. I was used. And my family and I have paid dearly for this," he said.
Diplomatic efforts to win Gross' release have so far failed.
"At this time, there are no indications that Mr. Gross will return to his family within the next decade," the lawsuit says.
Gross' health has also declined in prison. He has lost more than 100 pounds (45 kilograms), and earlier this year he developed a mass behind his right shoulder that an American doctor has said should be assumed to be cancerous unless proven harmless.
Gross' lead lawyer in the lawsuit, Scott Gilbert, said in a telephone interview that his client is a "well-intentioned, idealistic guy," not a "trained covert operative." Gross repeatedly noted risks, Gilbert said, but didn't know what to do about them. Gilbert said the government and DAI had fundamental duties to Gross that they failed to fulfill including properly briefing and debriefing him. He said the work Gross was doing should have been done by someone fully aware of the risks, not someone like Gross, who didn't even speak Spanish.
Also on Friday, Gross and his wife filed an approximately $10 million lawsuit in federal court in Maryland against the New Jersey-based Federal Insurance Co. DAI had purchased an insurance policy from the company that included a "wrongful detention policy" that covers Gross' imprisonment in Cuba.
The lawsuit says the company breached its contract by failing to pay expenses of the Gross family that are covered by the policy including legal fees and medical expenses. The lawsuit also says the insurance company has paid $2.3 million of the $5 million policy limit, some of it to DAI.
Associated Press writers Eric Tucker and Matthew Lee in Washington and Peter Orsi in Havana contributed to this report.
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