(Reuters) The National Football League and its players union argued in court on Friday over whether the suspension of the league's 2012 most valuable player, Adrian Peterson of the Minnesota Vikings, should be overturned.

U.S. District Judge David Doty said he would rule at a later date in the NFL Players Association challenge to the suspension of Peterson, which was handed down Nov. 18.

"I feel like I got a fair hearing today and I really appreciate all the support from my fans," Peterson said outside the courthouse. "It feels good to be in Minnesota."

A Texas grand jury indicted Peterson last September on felony child abuse charges after he whipped his 4-year-old son with a switch, a thin tree branch with its leaves removed.

He was placed on the Commissioner's Exempt List, taking him off the field with pay, until his legal issues were settled. After pleading no contest to a lesser charge on Nov. 4, the NFL suspended him without pay until at least April 15.

Peterson's suspension was upheld on Dec. 12 by arbitrator Harold Henderson, but the union feels Henderson, a former NFL executive hand-picked by Commissioner Roger Goodell to hear the case, was not impartial.

"He's not in any way neutral," attorney Jeffrey Kessler, who represents the union, told Doty.

The union also believes Peterson was unfairly disciplined by the NFL, since the incident with his son occurred in May - before the league's new personal conduct policy was unveiled.

The tougher policy, which NFL owners unanimously endorsed on Dec. 10, includes specific criteria on paid leave for people charged with a violent crime, including domestic violence, sexual assault or child abuse.

Daniel Nash, an attorney representing the NFL, told Doty retroactivity was "a red herring" and Goodell had the authority to impose the suspension. Henderson heard the evidence and found Peterson's suspension fair and consistent, he said.

Should Doty rule in favor of the NFL, Peterson could take the case to the 8th Circuit U.S. Court of Appeals.

Peterson, a six-time Pro Bowler, will be 30 years old next month and it is unclear whether the Vikings will want him back or allow the eight-year NFL veteran hit the open market. Free agency begins March 10 in the NFL.

When asked by a reporter if he wanted to return to the Vikings, Peterson replied, "Of course."

The NFL fined Peterson $4.1 million, or six weeks' pay, from his $11.75 million salary last season. His contract runs through the 2017 season, including $12.75 million for the upcoming campaign, but there is no guaranteed money remaining.

(By David Bailey; Writing by Steve Ginsburg in Washington; Editing by Grant McCool and Alan Crosby)