Coach Hue Jackson confirmed the team's decision to part ways with Pryor by saying, "We're moving on", but he declined to confirm the fight.
Pryor and receiver Ricardo Louis were involved, but Pryor drew the ire of Jackson when he did not stop as ordered, the source said. It is unknown what started the fight, or what Louis' eventual fate will be. Jackson called what happened an internal matter.
Pryor was behind second-year player Derrick Kindred and rookie Jabrill Peppers at safety on Cleveland's depth chart.
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Pryor reportedly was on the trade block after the Jets selected safeties Jamal Adams and Marcus Maye in the first two rounds of the 2017 National Football League draft.
The 25-year-old Pryor was selected 18th overall by the Jets in the 2014 NFL Draft and recorded 130 tackles with two interceptions over 44 games (three seasons) in NY.
"I feel like it was a great opportunity", Pryor said after the trade.