The council has been pressing the Scottish government on the dwindling financial settlement offered to the SIC over recent years.
Senior members met finance minister Kate Forbes during her visit to the isles today.
Among the topics for discussion was the level of funding to operate the inter-island ferry services in the isles, which has fallen to a level much less than what was hoped for.
The 2019/20 financial settlement from Edinburgh included £79.6 million in core revenue funding from the Scottish government – representing a 10.3 per cent drop since 2014/15.
And the settlement only included £5.2 million for inter-island ferry funding, against the council’s request for £7.9 million.
For 2020/21, the council says the operational cost of running Shetland’s inter-island ferries requires £9.49 million of revenue funding from the SNP administration.
The SIC’s current medium term financial plan has also identified a need to close a funding gap of £15.6 million by 2023/24.
Council leader Steven Coutts said: “I welcome the visit to Shetland by the Minister for Public Finance and Digital Economy and we’ve had some constructive discussions today.
“We’ve repeated our requirement for the Scottish government to honour their commitment to fully fund our inter-island ferries, as it does in other parts of Scotland.
“The working group initially set up by Derek Mackay has now concluded its work.
“We have a shared understanding of what full and fair ferry funding is.
“All that is left now is for the government to deliver fairness for Shetland and deliver the identified shortfall of £9.49 million in 2020/21.
“If we don’t receive this funding, this will have a very significant future impact on the delivery of services for the people of Shetland.
“The council is at the forefront of delivering services for our community.
“We must work hard to ensure the services we provide enable all in our community to achieve the best outcomes they can, but continued reductions in council funding from central government make the process very challenging.”