Speaking to the media on Tuesday, a day ahead of AEK's Greek Cup semi-final second leg match against Atromitos, Poyet further angered the club by revealing details of a private meeting he had held with Melissanidis.
"What he did was unacceptable, it was not the appropriate time to unsettle the team just hours before the semi-final,” Melissanidis told reporters.
"AEK has never leaked any information from any of our meetings with him and for him to talk to the press about the contents of our meeting is immoral.”
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While local media reported Poyet had been fired and would not be in the dugout for the match against Atromitos, AEK released a statement saying they would discuss the issue in full after Wednesday’s match.
“AEK was informed of Gus Poyet’s decision that he will not stay with the club after the summer on Tuesday evening," the club said.
"The important thing for AEK at the moment is the crucial semi-final with Atromitos, all of the other issues will be seen to after the match.”
Former Sunderland manager Poyet took over from Traianos Dellas last October on a deal until the end of the season with the option to renew for another two years.
Bankruptcy in 2013 had forced the club out of the Super League for the first time but they returned quickly under the ownership of Greek shipping and oil magnate Melissanidis.
'The Yellows' made an impressive return under Poyet and ended the regular season in second behind champions Olympiakos Piraeus. They will battle for Greece’s second Champions League spot in the playoffs against Panathinaikos, PAOK Salonica and Panionios.
Former Chelsea and Tottenham Hotspur midfielder Poyet, who played for Uruguay, has also managed Brighton & Hove Albion.
(Reporting by Graham Wood; Editing by Peter Rutherford)
