Medway councillors considering a 6.3% council tax rise are requesting an urgent meeting with the government about the area's "unique difficulties".
The council said there is a real risk that any rise over 5% could be capped.
Finance spokesman Councillor Alan Jarrett said local services would have to be cut if the government limits or caps the amount of council tax raised.
Members said Medway lost £4.755m in its government settlement and £0.995m was lost to repay previous years' spending.
The authority said it had, historically, "prided itself on low levels of council tax".
It also said the Audit Commission had given the council three stars for improving well.
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We are determined not to cut critical frontline services
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A statement from the council said a proposed revenue budget of £300m would require a council tax rise of more than 6% - or a 6.3% rise for a typical Band D property.
Mr Jarrett said: "Medway has a low base for council tax and has not enjoyed a favourable or even above-average financial settlement in previous years.
"We have a track record of prudent financial management and are determined not to cut critical frontline services."
A letter from the council leader, Councillor Rodney Chambers, and the deputy chief executive, Neil Davies, has gone to the government requesting "an urgent meeting".
Medway Council cabinet will look at the proposals on Tuesday, and the council is due to make a final decision on the budget at a meeting on 2 March.