Marcao said in a video on Twitter that he thought that he was right while arguing with 22-year-old winger Akturkoglu, but the Brazilian national admitted that he lost his temper at that moment.
"I am a human just like you, but could not show exemplary behavior. ... First, I apologize to Kerem's mother and father, ... then I also apologize to my brother Kerem for my behavior."
"I can understand that you may not want me (in the team) anymore. I respect all the decisions (by club) about me," Marcao added.
The Turkish club is expected to launch a disciplinary proceeding against him. Meanwhile, the Turkish Football Federation ruling on Marcao is also awaited.
Galatasaray beat GZT Giresunspor 2-0 on Monday to make a good start to the 2021-22 Turkish Super Lig season.
But the game saw a rare incident on football pitches as Galatasaray central defender Marcao headbutted and punched his teammate Akturkoglu in the second half, which led to a straight red card for Marcao over the violent act.
Marcao's assault overshadowed the game. He was under fire afterwards on social media and slammed by sports critics on TV as well.
A Galatasaray player since 2019, Marcos do Nascimento Teixeira -- commonly known as Marcao -- is one of the first team regulars and has a contract with the Istanbul club until 2024. He sealed a new contract in May to extend his stay.
Marcao helped Galatasaray win the Turkish Super Lig, Turkish Cup, and Turkish Super Cup in 2019.
He piled up 107 appearances for his club.
According to the German football data website Transfermarkt, Marcao had a €12 million ($14 million) market value.