Devon County Council is to receive an extra £4.3m from the government to minimise council tax increases.
Households may still face cuts in services
It is part of the £340m for English councils announced by the Chancellor in his pre-budget statement.
The council says the money is welcome but services are still under threat.
Council leader Brian Greenslade said even with the new money and a council tax rise of just 3%, £18m of cuts are still required.
Devon County Council says it needs a total £22m to fill funding gaps, which the £4.3m will go towards.
Brian Greenslade said: "I think people can see there is still a big gap for maintaining services and setting a council tax rise in single figures.
"It's very helpful, but it's not going to be a simple solution to all the problems of funding. There's quite a lot of work to be done yet.
"Even with this additional grant, if the council was to raise council tax by just 3%, it would still need around £18m in cuts in services to balance the books."
The government is adamant that it has been more than fair to local authorities and says large council tax increases will be neither justifiable nor acceptable.
It has warned that its prepared to cap any councils that insist on large tax rises.