Rangers have suspended Joey Barton for three weeks, six days after he was sent home from training following a heated argument with a team-mate.
The 34-year-old, who admitted he said some "inappropriate things" to fellow midfielder Andy Halliday, returned to Ibrox for a meeting on Monday.
A Rangers statement said the club and manager Mark Warburton felt all parties now needed "time and space".
It added neither the club nor Barton would make "any further statement".
Warburton was asked about the player at his media conference to preview Tuesday's meeting with Queen of the South in the League Cup but refused to disclose whether or not Barton will continue to be paid during his suspension.
"It's not for me to make any further comment other than what has been released by the club this morning," he said.
"I'm sure you can understand that from my position and the position of the club.
"The environment we create for the players and the staff is about giving respectful opinion. I'll never have a problem with a player knocking on my door to talk about a session.
"Do it in the right manner or else they'll get a flea in their ear.
"It's about being respectful with the way we deal with each other. I have no problem with players expressing opinions at all. It's how you deliver the message which will always be key to myself and my staff."
The verbal altercation between Barton and Halliday came as Rangers players reviewed their 5-1 loss to Scottish Premiership rivals Celtic.
Initially told to stay away from the club until Monday, Barton released a statement on Thursday in which he acknowledged he "did overstep the mark".
"Some of the things I said were inappropriate and for that I apologise unreservedly," he wrote.
He added he did not feel staying away from training was necessary.
Moments after posting the statement, he published a tweet he later deleted reading: "Apologising doesn't always mean that you're wrong and the other person is right. It means you value your relationship more than your ego."
The following day he gave a radio interview - not authorised by the club - in which he said he was sent home and Halliday was not because he also had a frank exchange of views with Warburton afterwards.
He described his suspension as "strange" and "wrong" and added he did not believe he had done anything to apologise for.
Barton joined Rangers in the summer on a two-year contract as a free agent, after turning down the offer of a contract extension at Burnley.
BBC Scotland's Richard Wilson:
"Barton's Rangers career would appear now to be effectively over. If the manager Mark Warburton felt reassured that the player could return to the squad without his authority seeming undermined, then Barton would still be available for selection.
"The player is due to begin a series of public engagements for the launch of his autobiography this week, at which he will inevitably be asked about his future at Ibrox.
"He is, by his own admission, a blunt and assertive figure in the dressing room and his short spell at Rangers has delivered little worth on the field. The team has already looked more convincing in his absence."