"I apologise to the fans present at Aguilera, from Bayonne and Biarritz, to the two teams and their staff, to the National Rugby League (LNR), the French Rugby Federation (FFR) and the rugby world in general," he said in a statement published on the Biarritz website.
"Under pressure for various reasons, I lost all control. I regret having behaved in such a manner during such a festival of rugby."
Biarritz said that they "accept" Lucien Harinordoquy's apologies and "hope that it will be the same for all the other parties involved".
Earlier on Wednesday, Bayonne president Michel Cacouault branded the incident "unacceptable" and announced that Bayonne would file complaints against both Biarritz and Harinordoquy senior.
The incident occurred in the sixth minute of Bayonne's 21-19 defeat at Biarritz in a fiery Top 14 match on Tuesday evening.
Harinordoquy's father raced onto the pitch from the stands and faced up to Bayonne flanker Jean-Jo Marmouyet after his son, a France international, got involved in a punch-up far from the action at the start of the Basque derby.
Harinordoquy senior's sense of family loyalty was brought to an abrupt halt by Bayonne fly-half Benjamin Boyet, who tackled him to the ground before Biarritz hooker Benoit August stepped in to restore order.
Christian Gajan, Bayonne's director of rugby, was outraged by Harinordoquy's father's behaviour.
"I find his behaviour deplorable, that he came onto the pitch to defend his son by boxing with Marmouyet at the beginning of the match," he said.
"You could have been forgiven for thinking it was a youth match between two local villages. It was a scandalous episode."
Harinordoquy junior, who is known as one of the tougher customers in the sport and is a veteran of three World Cups, chose not to comment.
LNR president Pierre-Yves Revol described the incident as "a first in professional rugby" and said that his organisation would conduct an investigation.