Ms Hagmann, an SNP councillor in Dumfries & Galloway, said local authorities were "acutely aware" of the ongoing cost of living crisis.
But she said increasing tax was not something councils wanted to do in a "complex landscape".
She said: "We have been consistent and clear that there should be no freeze on council tax and, importantly, there should be no cap either, because this is very much for local decision-making.
"The last thing local leaders want to do is raise council tax in a cost of living crisis, we are acutely aware of that, but we also need to protect those vital services."