Government and football authorities will convene later on Thursday to rule on the issue.
The Toumba stadium in Salonika resembled a war zone after hundreds of angry fans stormed the pitch and fought running battles with riot police in the closing minutes. PAOK owner Ivan Savvidis then withdrew his team from the cup.
"EPO condemns in the strongest possible way the extreme and unjustified, violent reactions which occurred before, during and after the cup match between PAOK and Olympiakos," it said.
EPO said it would examine the conduct of match officials and take appropriate action under the statutes.
In an apparent reference to the migrant and economic crises now convulsing Greece, the EPO statement said it would "not allow football to be involved in games and goals that go beyond the controversies on the pitch and be burdened with the problems of an entire society."
With Super League champions Olympiakos leading 2-1 in the 86th minute at a hostile Toumba stadium, PAOK were denied what looked like a clear penalty when Slovakia midfielder Robert Mak was felled by visiting keeper Stefano Kampino.
PAOK's players and supporters were incensed by the decision, prompting an explosion of violence as large groups of fans rushed onto the pitch, hurling flares and missiles before being dispersed by riot police.
It was the second time in Greece this season that a match has been stopped. The Athens derby last November involving Panathinaikos and Olympiakos was called off due to violent clashes between fans and police before kick-off.
Greek football has long been plagued by crowd trouble and PAOK can expect a hefty punishment, which will be more severe if the Salonika club carry out their threat of not turning up for the return leg in Athens on April 6.
Local media said Prime Minister Alexis Tsipras was expected to make a final decision later on Thursday on the possible suspension of competitive football in Greece after listening to the recommendations of Kontonis, the EPO and the league organisations.
(Editing by Gareth Jones)
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