The Belfast Education and Library Board had predicted a shortfall of £7.5m by the end of this financial year.
Board members claimed the Department of Education had promised extra money would be available and had let them down.
Speaking after the meeting, Ruane said she had made a bid for "additional funding" and added: "I am fully aware of the financial position of the board and my officials have been working closely with them to monitor and assess the situation and they will continue to do so."
Ulster Unionist councillor Jim Rodgers, chairperson of the Belfast Education and Library Board said: "I am reassured that her officials will continue to work closely with board officers and hope this process can be accelerated in order for the board to manage the current financial situation. By working together we can move towards protecting frontline services across the education sector in Belfast."
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