The cost of building a new Madras College has gone up by £8 million in the last year.
Construction of a new secondary school in St Andrews is expected to be complete by next summer.
But the anticipated price of delivering it has gone up to £58.27m from £50.17m this time last year.
The increase has been put down to a delay in construction caused by coronavirus restrictions and the deal with St Andrews University to acquire the land, understood to have cost the council £2.5m.
Provision of a new Madras College has hit a number of obstacles over the last decade, including the collapse of negotiations between Fife Council and the university in 2011 and a legal challenge which prevented it from being built on another site at Pipeland at a cost of £42.7m.
And North East Fife MSP Willie Rennie said: “The top priority must be to get the school open and these budgetary issues must not get in the way.”
However, the Scottish Liberal Democrat leader added: “We need a full explanation from the council so we can be sure that taxpayers’ money has been used well.
“If this is simply an accounting issue the council should explain that.
“If there are funding shortfalls because of the pandemic then there needs to a plan to overcome that including dialogue with the Scottish Government.”
St Andrews Conservative councillor Dominic Nolan said the rise in cost was not significantly concerning and added: “I am happy that progress is being made and applaud all those involved for their commitment and keeping on track through the pandemic.”
Fife Council senior manager Alan Paul confirmed that the cost of providing the new school may rise slightly as a result of delays caused by lockdown, which he said applied to most construction contracts impacted by Covid-19 and reflected Scottish Government guidance.
He said: “In addition, we’ve made an accounting adjustment to factor in the cost of the land swap agreed by the university.
“We are still on track for staff and pupils to move into their state-of-the-art new school in August 2021.”
A report by education and children’s services executive director Carrie Lindsay and Eileen Rowland, executive director of finance and corporate services, said all but critical construction projects went on hold in March.
It said: “It is likely that Covid-19 will impact on project costs and will extend all project delivery dates as contractors will require to make adjustments to working arrangements to accommodate new requirements, such as social distancing.
“Some claims from contractors have already been received in relation to closing down, maintaining and re-opening sites and also in relation to preparation for work on site recommencing, for example in relation to Madras College.
“Monitoring of the impact of these additional costs and timescales is ongoing and it is likely that the overall scale of these additional costs will be clearer in the coming months.”
When councillors authorised the exchange with the university of the South Street building for 18 acres at Langlands in 2017 they were told the deal would also cost them £2.5m.
South Street is being leased until the new school’s completion and the school’s Kilrymont campus was put up for sale for redevelopment.
Meanwhile, there has been a delay in the delivery of a £1m extension to Masterton Primary School, in Dunfermline.
Work on the extra two classrooms is to start in the autumn, and is expected to be complete by spring next year.
The additional space is needed to accommodate pupils, with approval for construction of another 400 houses in the area.