The next move is how the PGA Tour chooses to respond. It does not make public any discipline.
O'Hair said after his second round Friday at The Players Championship that Sabbatini sent him a text last week asking O'Hair to call so they could talk it over.
"He apologized and I apologized," O'Hair said. "Life goes on."
According to multiple players and officials, the New Orleans incident was the second time this year that Sabbatini has run into trouble because of his behavior on the golf course. At the Northern Trust Open in February, he is said to have spoken harshly to a teenage volunteer who was trying to help him find a lost ball.
O'Hair has not said publicly what triggered their argument in New Orleans, only that it was not about slow play.
"I wish I would have handled it better," he said. "I could have waited until after the round."
Sabbatini said he "resolved" the issue with O'Hair and the last thing any player wants to face on the golf course is tension with other players. Sabbatini shot a 71 on Friday and was tied for 11th, four shots out of the lead. O'Hair made the cut for the first time in six tournaments after rounds of 71-71 and was eight shots behind.