The 28-year-old Brazilian has agreed to apologise to his Spanish colleague for the training-ground fight they were involved in last Thursday
The pair clashed during a training session last week and both players have subsequently been fined for their involvement in the row.
Melo, though, has accepted responsibility for the fracas and is now keen to put the whole affair behind him and help Galatasaray maintain their title charge.
"I've spent a horrible week with my family and cried for a whole day, but I have agreed to apologise to Riera and my team-mates,” he told Fanatik.
"But my team-mates' attitude throughout all of this has made me very happy - it's shown that we are a family.
"Nobody was expecting it to happen. Everybody knows how much I regret it. It's the first and last time that this has happened in my career.
"I came here to write a story, and make a good contribution. The next goal is to become champions."
Galatasaray are currently five points clear at the top of the Super Lig ahead of this weekend's meeting with Besiktas.