Local authority has accepted a £9m grant from the Scottish Government in order to keep council tax at current levels.
Conservative group leader Thomas Kerr has written to the city treasurer calling for a council tax 'moratorium'.
The measures are part of a huge economic stimulus package announced by the UK Government.
Councils around Scotland are setting their budgets and council tax rates ahead of the new financial year.
Local authorities in Scotland's two biggest cities agreed their budgets on Thursday.
Jackson Carlaw and Michelle Ballantyne are both hoping to succeed Ruth Davidson at the helm of the party.
