Pastoor, who was Van Basten's assistant at the club, swapped roles on Tuesday when the former European Footballer of the Year said he could no longer continue as head coach but would stay on as assistant.
Pastoor left AZ after failing to come to an agreement over a new contract for his new role, the club said on Thursday.
"In the last days we have had several discussions with Alex," technical director Earnest Stewart said in a statement on the club's website.
"After the decision to make Marco van Basten assistant coach, we had the intention to promote Alex to head coach. We made him an improved offer but he did not agree to it. In our last discussion we came to the conclusion it would be better for us to part ways."
AZ said they would be seeking a new coach as quickly as possible.
On Tuesday, Van Basten announced his intention to stand down and said he would never take a head coach’s role again.
He had signed a two-year deal with AZ at the start of the season but heart palpitations caused by stress had seen him miss the last two matches of the club, which Pastoor had taken charge of.
(Reporting by Mark Gleeson; Editing by Amlan Chakraborty)
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