The council's president, Hamish Saunders, works in Russell McVeagh's Auckland office and said he was unable to comment.
Many of the council's regional conveners are also Russell McVeagh lawyers.
The national debating competition has been known as the "Russell McVeagh New Zealand Schools Debating Championships", but the firm's name was removed from the competition's Facebook page today.
All six NZ law schools also said last week that they would stop hosting Russell McVeagh on their campuses until the firm completed its investigation of the alleged sexual harassment.
The allegations concerned sexually inappropriate behaviour towards young female law clerk students in Russell McVeagh's Wellington office more than two years ago.
Students at Tauranga's Aquinas College had pulled out of the competition after finding out the competition was sponsored by Russell McVeagh.
Principal Matthew Dalton said two of his debating students came to him with their concerns last week and asked if he would support them in withdrawing from the competition.
Dalton said the school emailed their concerns to the NZ Schools' Debating Council which replied the competition had dropped sponsorship from the law firm nationwide.
The principal said the college felt morally and ethically obliged to withdraw from the competition and he was proud of the student-led position on the matter.
"I can be proud of the two students who came to me," Dalton said.
"I am proud of them for taking that stance. They obviously wanted to take part in the competition, but their feelings trumped that."