The withdrawals have left New Zealand with three combinations in endurance in the Games in Kentucky, severely damaging the country's chances of team honours.
The Endurance Board, in a statement to members, noted the public discussion and debate around the withdrawals and voiced fears it could damage the sport's standing.
It said it wanted to reiterate to members that the Endurance Board held no authority over ESNZ High Performance and retained no position of influence over endurance high-performance selections or selection criteria for the Games.
"The Endurance Board has expressed its concern to the ESNZ chief executive at the lack of forthcoming and timely communication in regard to the withdrawals, and has asked for the Endurance Board to be given a better understanding of the 'events' and procedure leading up to the formal announcement of the withdrawals."
It continued: "The Endurance Board would like to express to members their concern [as] to the damage that the sport might suffer due to the consistent negative discussion and debate being held in the public arena and would ask that those involved give first consideration to what is good for the sport of endurance.
"The Endurance Board does take this opportunity to acknowledge all of the correspondence in regard to the WEG Team that has been sent to them.
"The Board of Endurance would like to confirm their ongoing support and encouragement to the remaining Endurance WEG Team as they represent New Zealand Endurance on the world stage."