Fairfax County supervisors for the second time killed a plan by school officials to buy and renovate a new administrative building at a cost of nearly $100 million, deriding the proposal as ill-timed amid sharp cuts to both school and county spending.

The Board of Supervisors on Monday unanimously rejected the proposal, which would have allowed the public school system to consolidate offices from around the county into one building next to its existing headquarters on Gatehouse Road. The proposal needed the supervisors’ approval to move forward.