OM said in a statement on their website that English midfielder Barton and French defender Abdallah had a "verbal clash" during a public training session, without elaborating.
"During my career, I've seen 30 or 40 clashes on a training pitch," Barton told OM TV.
"These clashes should be dealt with in private. We are competitors... and sometimes we go a little bit too far. The most important thing is to make peace and move on - that's what happened yesterday."
Barton arrived in France on loan from QPR following a colourful career in England during which he spent two and a half months in prison for assault during a night out in Liverpool.
At the time of the attack, he was already on bail for attacking former Manchester City team-mate Ousmane Dabo and he also stubbed out a cigar in the eye of a youth team player at the club in 2004.
"It's certain that where I am, there is always a little bit more noise and exaggeration," Barton said. "I'm aware of that, that's why I said yesterday: 'let's stop it, calm down. If there's a problem, let's deal with it in private'."
‘So many times when we played Manchester United, arguments would start before the first whistle had even blown – the players would try to kill each other with their eyes’ Former Arsenal star remembers famous Premier League rivalry
Bizarre Jose Mourinho statement aims to pre-empt punishment after Fenerbahce boss clashes with Galatasaray counterpart
