Lawyers for the widow of Chris Kyle want a new trial. Former Gov. Jesse Ventura wants the $1.8 million award he won in his defamation case against the estate of the author of “American Sniper” to stand.

The two sides got 20 minutes each to lay out their arguments Tuesday before a three-judge panel of the Eighth U.S. Circuit Court of Appeals in the federal courthouse in St. Paul.

Afterward, Ventura spoke his mind to a crowd of reporters outside the courthouse. “It’s my name and my reputation that I’ve spent 40 years building,” he said. “If they order a new trial, we’ll go at it again.”

The judges grilled lawyers for Kyle’s estate and for Ventura in a case that has garnered attention from major media organizations and a dozen First Amendment scholars, who say that the verdict was unjustified and that it could have a chilling effect on journalists.

The case pits Ventura, the former wrestler and governor of Minnesota from 1998 to 2002, against Taya Kyle, the widow and executor of the estate of the late Chris Kyle, whose bestselling memoir, “American Sniper,” was the subject of Ventura’s defamation lawsuit.

Kyle wrote that in 2006 he punched Ventura in a California bar where a wake for a Navy SEAL was in progress, after Ventura, a former SEAL, made derogatory remarks about the Iraq war and then-President George W. Bush and said the SEALs “deserved to lose a few.”

Ventura said that he was at the bar, but that the incident was a complete fabrication. A federal jury, by an 8-2 vote, sided with Ventura, awarding $500,000 for defamation and more than $1.3 million for “unjust enrichment” — a portion of the profits reaped from the book.

Kyle attorney: ‘No excuse’

The estate’s attorney, prominent Washington, D.C., First Amendment lawyer Lee Levine, argued that no court has ever awarded money to a defamation plaintiff for unjust enrichment based on a published falsehood. Further, he said, the instructions to the jury were flawed and there was no clear and convincing evidence that Kyle’s account was untrue.

Levine backed his argument with the testimony of sisters Rosemary and Laura deShazo, who were at the bar that day. Rosemary deShazo said she heard a “lose a few” remark by Ventura, while her sister said she saw a punch being thrown. Levine said neither woman was drunk.

Levine also said that a new trial was necessary because in his closing argument, Ventura’s lead lawyer, David B. Olsen, improperly said the insurance company for the publisher of “American Sniper” would be “on the hook” for any money the jury awarded Ventura, meaning Taya Kyle and the estate would not have to pay it.

“To be blunt, there is no conceivable excuse for this,” Levine said.

Presiding Appeals Court Judge William Riley asked Levine why attorneys for the estate didn’t object immediately when Olsen mentioned insurance. Levine said they did so after closing arguments when they moved for a mistrial.

Riley revisited the insurance issue during Olsen’s arguments for Ventura on Tuesday, saying: “It’s one phrase in the heat of the moment and lawyers step over the line, but in my experience that was over the line.” Olsen responded that his “on the hook” quote was taken out of context, noting that a reference to the publisher’s insurance was included in the contract for the book that was shown to the jury.

Olsen: ‘None of it happened’

Olsen told the panel that the verdict for unjust enrichment is justified because Kyle made money off what was found by a jury to be a lie in its entirety.

“This incident, written and talked about by Chris Kyle, did not occur,” said Olsen. “Gov. Ventura testified flat out, ‘I didn’t say those things, I wasn’t hit, I wasn’t humiliated by showing up to a graduation ceremony with a black eye. None of it happened.’ ”

Olsen said Ventura’s side produced witnesses at the trial who said that Ventura did not make the remarks quoted in the book and that there was no fight. He said photographs of Ventura taken after the incident showed not a mark on him.

After the hearing, Ventura bristled when he was asked by a reporter what he thought of the argument that “unjust enrichment” should not apply in defamation cases.

“Excuse me, the book made $40 million. As soon as they defamed me, the presale of this book was 4,000. When [Chris] Kyle went on TV that day [two days after the book was published], it jumped 100,000 in one day,” Ventura said. “Put it in this context: When you shoot a rocket to outer space, there has to be a booster rocket on it to get it into space. … I was the booster rocket in this book that propelled it to No. 1.”