The council followed the Wake County Board of Commissioners in adopting the resolution, which stands in opposition to recent actions by the Board of Education.
"We need to do anything in our power to stop the school board," Mayor Charles Meeker told the council.
Meanwhile, the school board majority voted again Tuesday in favor of a resolution restating its commitment to voluntary desegregation of schools.
The board wants to move away from the school system's decade-old student assignment policy that buses students to ensure socio-economic balance at schools across the county.
Members in favor of the resolution have said they will develop a policy of community-based assignments which will allow more students to attend school closer to home.
Opponents of the change say they fear it will lead to re-segregation and pockets of good schools and bad schools.
The school board members who voted in favor of the change insist that they have no plans to segregate students.
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