ST. PAUL, Minnesota (AP) — An attorney for former Gov. Jesse Ventura asked a federal jury Tuesday to award him millions in damages for what he claims is a lie in a slain military sniper's memoir. But an attorney for the estate of the late author said Ventura has failed to prove he was defamed in the book "American Sniper."

Chirs Kyle, who had been a Navy SEAL, wrote best-seller in 2012 about his time as a sniper who broke records with his aim. The book also describes a brief encounter in which he punched a man he named "Scruff Face." Kyle later identified the man as Ventura, a former professional wrestler-turned-politician.

The jury deliberated for about 4½ hours before stopping for the day and was to return Wednesday to continue.

Kyle, who served several tours in Iraq and regarded himself as the most lethal sniper in American military history, was killed at a gun range in February 2013, allegedly by another Iraq War veteran.

Ventura, a former SEAL himself, says the book libeled him with its claim that the former governor made remarks critical of Navy SEALs. Ventura, who was also a movie actor before being elected governor for one term in 1998, testified that his income as a television personality fell sharply as job offers dried up in the wake of "American Sniper."

Ventura's attorney, David Bradley Olsen, said in his closing argument that he believes Kyle's estate has earned more than $6 million from the book. He suggested jurors award Ventura from $5 million to $15 million to compensate for what he said was the harm to Ventura's reputation.

Olsen also said Kyle's claims made Ventura a pariah in the community that mattered most to him — the brotherhood of current and former SEALs.

But John Borger, an attorney for Kyle's estate, argued earlier that Ventura didn't prove that the story was false. Borger also rejected Ventura's claim that the book hurt his earning potential. He said Ventura's star had faded, and his reputation was harmed by his pursuit of the lawsuit.

Kyle's widow, Taya Kyle, had become executor of his estate with control over proceeds from book royalties and movie rights that have topped $3 million. A judge allowed Ventura's lawsuit to proceed against the estate.