The alleged comments referred to the first meeting between the crew of the Endeavour and Māori at Tūranganui-a-Kiwa/Gisborne in October 1769, when nine Māori were shot and killed, and three young boys kidnapped.
Pressure has been mounting in the Gisborne community for the alleged councillor to come forward, as Akuhata-Brown did not name them in her column.
Deputy mayor and chair of the code of conduct committee Rehette Stoltz said both councillors were facing a code of conduct review.
"As signatories to our code of conduct we expect our elected members to act with the utmost integrity and respect in any forum in which they participate," Stoltz said.
"We will be working through a process to determine whether the principles of our code of conduct have been breached.
"I am disappointed with what has happened here and any breach will be dealt with swiftly and accordingly."
Akuhata-Brown declined to comment, citing the code of conduct review.