The council has requested a meeting with Serco representatives ahead of the planned weekend strikes which are due to begin on Friday.
SIC leaders say they are concerned for the “crippling effect” the strikes will have on people in the isles.
They have written to Serco NorthLink’s managing director, Stuart Garrett, requesting an immediate “face-to-face” meeting to discuss the industrial action.
Political leader Gary Robinson said: “Shetland Islands Council is very concerned about the threat of strike action and the crippling effect this will have on the people of Shetland should it go ahead. We will do everything we can to try to help avert the situation.
“I’ve already had a telephone conversation with Stuart Garrett on this matter and I’ve written to him outlining our concerns and requesting an immediate face-to-face meeting.
“A further meeting with their operations director, Captain John Ferguson, is expected to take place in Lerwick this week.”
As things stand Serco’s Shetland to Aberdeen service will stop for 24 hours from 8am on Friday. The same will happen on the two following Fridays – 21st and 28th December.
The Orkney to Scrabster route will also be affected on the same dates. Meanwhile the Aberdeen-Orkney-Shetland service will also face a full day stoppages on Sundays 16th, 23rd and 30th December.
The action is being taken over plans to cut up to 36 jobs from the North Isles service.