Earlier this week, actor and comedian Michael Rapaport posted private messages that he said Durant had sent him -- which included threatening language and anti-gay and misogynistic slurs.
Coach Steve Nash said the organization had a conversation with Durant about the language used in the exchange, and the Nets star apologized Thursday.
"I'm sorry that people seen that language I used," Durant said. "That's not really what I want people to see and hear from me, but hopefully I can move past it and get back out there on the floor."
Durant has missed the Nets' past 21 games with a hamstring injury. He is averaging 29.0 points, 7.3 rebounds and 5.3 assists per game this season.
ESPN's Malika Andrews contributed to this report.