He was also interim assistant coach - alongside Des Buckingham - for part of last season.
A club statement on Thursday said that "both parties agreed it would be in the best interests of the club to make a decision swiftly, thereby allowing any potential replacement the opportunity to familiarise themselves with the current player group for the remainder of the 2017/18 A-League campaign as the club looks to rebuild for next season."
Kalezic added that the decision was made in the best interests of the club.
"Since the club and I weren't able to find mutual agreement on how to proceed in the future, my professional belief is that the next coach should be provided with [the] opportunity to lead the team for the remaining of the season in order to have enough time to create his opinion about current squad and his own action plan on how to proceed in the season to come."
"I have had [a] great experience in New Zealand – I came with big determination and energy for this project and I continue to believe that success can come for this football club."
Even though he made some important changes off the field and in the backroom, Kalezic was a failure on the field. He was in charge for 21 A League games, with four wins, five draws and 12 losses.
The Phoenix remain bottom of the table, and are heading for their worst season in terms of points gained.
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