Its Cabinet met on Tuesday and recommended to Council amended budget proposals for 2020-21.
After the meeting the Cabinet Member for Finance and Resources, Cllr Adam Stokes, said essential services would not be affected by budget changes.
He said: "The original budget was approved on 2 March but within a few weeks the country was facing the worst health crisis in a lifetime and the council has felt the impact of that.
"Given the volatility that has been experienced since the start of the financial year, it is inevitable that the budget framework no longer reflects or meets current operational issues and demands. Income is no longer reaching budgeted levels and we are also facing new cost pressures."
Factors including income loss and anticipated cost increases have led to an increase in budget requirement of £4.1 million, which falls to £2.4 million when confirmed Government support is taken into account.
The Government is also introducing a scheme to compensate councils for relevant, irrecoverable losses in 2020-21 under which local authorities bear the first 5% of losses compared to their expected income, and the Government supports those worst affected with 75p in every pound of losses beyond that. Indications suggest that a contribution of around £1.4m could be available to SKDC.
The Cabinet voted in favour of an amendment proposed by the portfolio holder for Commercial and Operations, Cllr Dr Peter Moseley, that there should be a £93,000 adjustment to the budget to cover a market supplement that will bring the pay of waste operatives in line with other local authorities.
The change means SKDC will have a predicted budget deficit of around £1.3 million.
SKDC can, if necessary, call on a budget stabilisation reserve set up to respond to unexpected changes and ensure a balanced position is maintained with no detrimental impact on essential services.
Cllr Stokes said: "South Kesteven District Council is in a strong position to cope with the financial impact of Covid-19. The use of the budget stabilisation reserve will only be considered as a last resort after other proactive cost avoidance and reduction initiatives have been considered.
"These include the continual review of expenditure to identify reductions, review of staffing vacancies and prioritisation of key staffing recruitment, and the acceleration of savings, transformation and invest to save proposals."