"I'm sorry for this incident. I apologize to my teammates, to the fans of this organization. It was definitely an unfortunate incident," Jackson said.
"I worked hard this summer to get myself physically and mentally ready for the season and to come out and help this team to be the best it can be this year."
Jackson was at the club with teammates Jamaal Tinsley, Jimmie Hunter and Marquis Daniels when an argument led to the melee, in which Jackson fired a 9mm handgun after being hit by a car.
"I'm definitely blessed to be here today," Jackson said. "I didn't really think I'd be waking up the next morning after I got hit by a car."
Indianapolis police arrested a 23-year-old Deon Willford in connection with the incident and charged him with criminal recklessness, leaving the scene of an accident and driving without a license.
Jackson said he hopes to put the matter behind him.
"I understand. I definitely take responsibility for my actions and everything that I have done. For that I am sorry and I apologize for it," said Jackson.
"Hopefully I can just move on from this and continue to be the player this team wants me to be and this organization wants me to be and kind of put this behind me. I hate that it happened. But I am sorry for it."
Jackson was suspended for 30 games in 2004 after taking part in a brawl between Pacers players and Detroit Pistons supporters during a game at Auburn Hills, Michigan.
"I haven't been in any trouble in my career before the Detroit incident 'til now. I haven't had a criminal record or anything. So I'm just happy to be back on the court, happy that I'm alive and able to be with my teammates and my family.
"Hopefully I can get this behind me and move on and try and get ready for this season."