The private investment firm and Akzo have been at odds since Akzo - in which Elliott owns a 3% stake - rejected two takeover bids from United States chemicals manufacturer PPG Industries, saying they undervalued the company.
Elliott has been trying to ramp up the pressure on Akzo to negotiate a potential sale to USA manufacturer PPG Industries, after Akzo rejected an improved €22.4bn (£19bn) cash and stock offer last month.
According to Akzo, Elliott and other shareholders have requested a meeting to dismiss Mr. Burgmans.
An Akzo Nobel spokesman said the company strongly supported the chairman and would respond to the request within 14 days as required by Dutch law.
Elliott, which became an Akzo shareholder in December, is known for its aggressive moves. Burgmans is viewed as an opponent to the deal but Elliott has pressed the company to engage with PPG.
PPG's most recent offer for Akzo was 90 euros per share which includes a dividend.
"It is only through engagement that Akzo Nobel can determine if PPG is prepared to bid at a level that provides adequate consideration to shareholders".
Akzo last month rejected a $24 billion offer from PPG after rebuffing an earlier $22 billion bid.
In a communication seen by Reuters, Gordon Singer of hedge fund Elliot Advisors accidentally included a representative of AkzoNobel (AKZO.AS) in an otherwise internal distribution list on Tuesday.
Akzo said it turned to the Dutch financial regulator after it became aware Tuesday that Elliott meant to share with PPG potentially price-sensitive information about the demand. The investor added that it has met with PPG as one of the Dutch company's top 20 shareholders.
Elliott said it and affiliates hold a stake in Akzo Nobel of more than 3 percent, and it's backed in calling for an EGM by investors holding more than 10 percent. Akzo's Dutch corporate structure gives its board wide latitude to control and block takeovers.
However Akzo CEO Ton Buechner has argued his plan is better for "all stakeholders" including employees, customers, and the environment.