The private investment firm and Akzo have been at odds since Akzo - in which Elliott owns a 3% stake - rejected two takeover bids from USA chemicals manufacturer PPG Industries, saying they undervalued the company.
In its response to the call for the removal of Mr Burgmans, Akzo revealed that it has reported Elliott to the Dutch authority for the financial markets, and called on the hedge fund to "clarify its relationship" with PPG.
Elliott Management owns 3.25% of the equity interest in Akzo Nobel via its United Kingdom division.
"Shareholders have a legal right under Dutch law to put a proposal to dismiss Mr Burgmans onto the EGM agenda", Elliott said in a statement on Wednesday.
Akzo said it would examine whether to hold the extraordinary meeting and respond within a required 14-day period, though spokesman Andrew Wood said Dutch corporate law gives it the power to not hold a meeting if it isn't in the interests of shareholders and the company.
While PPG acknowledged it met with Elliott as well as other Akzo shareholders in the weeks since Akzo rebuffed two offers to buy it, "There has not been any, and there are now no agreements or arrangements, in whatever form, between PPG and Elliott Advisors", PPG said in a statement.
Akzo last month rejected a $24 billion offer from PPG after rebuffing an earlier $22 billion bid.
Elliott wants Akzo to consider a $26.3 billion takeover bid from Pittsburgh, Pa. -based PPG Industries and thinks Burgmans is blocking the deal. Elliott added that it is "aware of its various regulatory obligations, including obligations related to handling price-sensitive, or potentially price-sensitive, information".
"We fail to see how Akzo Nobel could have a meaningful discussion with shareholders about its plans for a potential separation of the specialty chemicals business while the alternative of a transaction with PPG is being effectively disregarded from the outset", Elliott said in a letter to Akzo's management, according to Reuters.
Akzo has said it can generate more value for shareholders on its own.
It was not clear what rules, if any, the shareholder and PPG might have violated.