Ivan Savvidis, president of PAOK, said in a statement posted on the Thessaloniki club's website on Tuesday that he had meant no harm by his actions.
"I am very sorry over what happened. I clearly had no right to enter the field of play in this fashion," the statement said.
Savvidis, a Greek-Russian billionaire who is both the president and owner of PAOK, stormed out onto the pitch in the 90th minute on Sunday after a goal that would have won his team the top-of-the-table clash against Athens side PAOK, but was disallowed for offside.
"I'd like to apologize to the fans of PAOK, to all Greek fans and to the international football community," he added. "Believe me, I had no plans to quarrel with the referee or the opponents, and I clearly did not threaten anyone."
Instead, the 58-year-old Savvidis said his intention had been "to protect tens of thousands of PAOK fans from provocation, clashes, human victims."
Play in the Greek first division has been suspended over the incident and police want to discuss the matter with Savvidis, not for being in possession of a gun, for which he has a license, but for the pitch invasion, which is a criminal offence although it carries no prison sentence.
The incident has been condemned by both football's European governing body, UEFA, and the world governing body, FIFA, which issued a statement threatening to impose sanctions if all sides fail to take "immediate steps" to end the "unacceptable situation in Greek football."
pfd/mds (dpa, AFP, AP)