Council tax and rent payments in Fife could be cut or deferred, Fife Council co-leaders David Alexander and David Ross said.
Hundreds of staff are understood to be off sick or in self isolation, but guidelines have been put in place to ensure the vast majority can work from home.
In a joint statement, the co-leaders said: “We have been preparing for this virus arriving in Fife, and our services have been working hard to identify those in our communities who are most vulnerable. We will make sure that they continue to get the support they need.
“For the rest of Fife, there will be many changes to the services you receive in the coming weeks as we prioritise staff and resources towards the most critical services.
“Our staff are under incredible pressure and they themselves are not immune to the virus. We need you to be patient.
“As a society we have to look after those who are most in need first. This is a message which is very clearly already out there.
“We can see how our communities are already pulling together at this time. We and our third sector partners are being inundated with offers to help.
“We are very grateful for all these and in the coming days and weeks we will be looking at how, where and when we can best use that support.”
“We are helping to support and co-ordinate local action,” the statement continued.
“Council staff are currently contacting local groups to map the activity which is taking place in each area. This will also allow gaps in support to be identified.
“For those who are already struggling financially through minimum wage jobs, zero hours contracts, unemployment and for those who are self-employed or contract workers we understand that there is a significant level of anxiety.
“We’re going to be flexible with council tax and rent payments, allowing people to reduce or defer them, depending on individual circumstances.”