ST. PAUL — An attorney for Jesse Ventura asked a federal jury Tuesday to award the former Minnesota governor millions of dollars in damages for what he claimed is a lie in a memoir by the late military sniper Chris Kyle.

Ventura testified during the two-week trial that Kyle fabricated a passage in his 2012 best-seller “American Sniper” about punching him in a California bar in 2006 after Ventura allegedly made remarks insulting Navy SEALs. But Kyle said in testimony videotaped before his death last year that his story was accurate.

In his closing argument, Ventura attorney David Bradley Olsen said he believes Kyle’s estate has earned more than $6 million from the book, and suggested that $5 million to $15 million would be reasonable compensation for what he said was irreparable harm to Ventura’s reputation.

“The verdict will tell the world Chris Kyle’s story was a lie,” Olsen said.

The jury deliberated for about 4 1/2 hours before stopping for the day and was to return Wednesday to continue.

Olsen said Kyle’s claims that Ventura said he hated America, thought the U.S. military was killing innocent civilians in Iraq and that the SEALs “deserve to lose a few” had made him a pariah in the community that mattered most to him — the brotherhood of current and former SEALs.

“One-point-five million people have bought the book,” he said. “Millions more heard Fox TV trash Jesse Ventura because of it. And the story went viral on the Internet and will be there forever.”

But defense attorney John Borger told jurors in his own closing argument that Ventura failed to prove his claim that Kyle made up the story, and didn’t prove he suffered financially because of the book. He said the 11 witnesses presented by the defense “tell a compelling and consistent story” that backed Kyle’s version.

“Jesse Ventura is either deluding himself or intentionally telling you things that just aren’t true,” Borger said.

Legal experts have said Ventura has to clear a high legal bar to win, since as a public figure he must prove “actual malice.” According to the jury instructions, Ventura had to prove that Kyle either knew or believed what he wrote was untrue, or that he harbored such serious doubts that he acted with reckless disregard for the truth.

U.S. District Judge Richard Kyle, who is not related to the author, told the six men and four women who began considering the case around midday that they weren’t charged with determining whether Ventura was punched, but rather whether he was defamed by the remarks Kyle attributed to him.

Kyle, regarded as the deadliest military sniper in U.S. history, included a brief account in his 2012 best-seller of a confrontation at a bar in Coronado, California, with a man he called “Scruff Face.” In promotional interviews, Kyle identified the man as Ventura, a former SEAL who became a pro wrestler and movie actor before being elected for one term as Minnesota governor in 1998. Ventura was in Coronado for a SEAL reunion and graduation ceremony.

Olsen said inconsistencies in testimony from defense witnesses about what happened the night of Oct. 12, 2006, were so serious that their stories couldn’t be trusted. He also pointed out that people who were with Ventura that night testified that the alleged confrontation never happened. And he said Ventura would never have said any of the remarks attributed to him because he remains proud of his and his parents’ military service.

“The statement is completely out of character for Jesse Ventura. He never said anything like that in his life, and he never will,” he said.

Ventura testified that his income as a television personality fell sharply as job offers dried up in the wake of “American Sniper.” Borger said Ventura’s career as an entertainer was in decline well before that.

“Jesse Ventura’s income has declined because his star has faded, not because of Chris Kyle’s statements,” Borger said. He added: “What really harmed his reputation was bulling through this lawsuit after Chris Kyle’s death.”

Kyle was slain at a Texas gun range last year. His widow, Taya Kyle, is executor of his estate with control over proceeds from book royalties and movie rights. Judge Kyle allowed Ventura’s lawsuit to proceed against the estate.