"The discussion we had involved some sharp disagreements about the game and some harsh words were said," Barton posted on his Twitter account.
"There were only words involved in the disagreement, nothing else. Nevertheless, some of the words used did overstep the mark.
"As someone who communicates directly, I accept that some of the things I said were inappropriate and for that I apologise unreservedly."
The 34-year-old said though he did not agree with the manager's, he would respect it, and will return to training on Monday.
"The manager felt that my words were inappropriate and asked that I take some time out to reflect on what was said," Barton said. "He judged that it was best if I didn't report for training again until Monday.
"I regret what happened and on Monday I will report for training and I will do what it takes to help the team draw a line under it so that we can go back to the task at hand."
Barton is no stranger to controversy, making headlines for the wrong reasons during a career in which he also played for French side Marseille.
He broke a pedestrian's leg while driving his car in 2005 and was jailed for six months in 2008 after admitting assault and affray.
Barton's disciplinary record also includes bans for violent conduct and fines and suspensions for altercations with fans and team mates.
Rangers host Ross County in their next league fixture on Saturday.
(Reporting by Nivedita Shankar in Bengaluru; editing by Sudipto Ganguly)
