Ministers have been accused of a cover-up after culture secretary Fiona Hyslop admitted the project team had raised the alarm in April last year.
But it was not until January that Dundee City Council, a key partner in the project, admitted that the budget had risen dramatically from £49 million to £80m.
Ms Hyslop also admitted the government was given the new price tag on 18 December, almost a month before it was finally announced.
Council leaders have already approved an inquiry into the ballooning price tag for the attraction, which is now not due to open until 2018 – four years later than planned.
But Scottish Labour said the latest revelations, which emerged in a parliamentary answer to shadow culture secretary Claire Baker, demonstrated a “clear need” for the government’s role to be properly investigated.
The government, the council and the Heritage Lottery Fund (HLF) have all had to plough millions of pounds more money into the project to ensure that work can get under way next month to try to avoid any further cost increases.
Attempts to instigate a parliamentary inquiry – like the ongoing one into the state of the film and TV industries – have been rebuffed, with opposition councillors claiming SNP members on the education and culture committee had “kiboshed” the probe.
Ms Hyslop has spoken out against the need for a full probe into the museum project, saying it would cause further “uncertainty and delay”.
Audit Scotland has also resisted calls to launch its own investigation into the handling of the museum project, which is the centrepiece of the city’s
£1 billion waterfront development.
The city council has charged a former chairman of Rangers Football Club, John McClelland, with conducting its independent inquiry, although it has already committed an additional £6.5m to the project.
Ministers have approved an additional £10m and could provide an further £12.6m loan, similar the one which rescued the long-delayed project to overhaul the St James Centre in Edinburgh.
The HLF recently agreed to increase its own contribution from £9.4m to £13.9m.
Ms Baker asked the Scottish Government when it was made aware of the delay and rise in cost for the Dundee V&A project.
Ms Hyslop replied: “Dundee City Council kept the Scottish Government informed, within the bounds of commercial confidentiality, of the contract negotiations.
“As part of this, in April 2014, the council informed the Scottish Government that the initial estimate of the price would not be met and that there was a potential impact on the site mobilisation planned for August 2014.
“The contract price of £80.11m published by Dundee City Council on 16 January was shared with the Scottish Government on
18 December 2014.”
Ms Baker said: “The Scottish Government knew as far back as April 2014 that the V&A was heading for both a dramatic overspend and further delay but kept that a secret. There is a clear need for an inquiry which includes the Scottish Government.
“The SNP-led education and culture committee must now reconsider the decision not to hold an inquiry and I will be pressing them to do so.
“The council’s investigation is welcome but it won’t cover the role of the Scottish Government.”
A Scottish Government spokesman said: “The Scottish Government was informed in April 2014, within the bounds of commercial confidentiality, that the initial cost estimate for the V&A Dundee project would not be met. Disclosure of this information at that stage would have prejudiced substantially the commercial interests of Dundee City Council as the contracting authority.”
A spokesman for Dundee City Council said: “A thorough and rigorous review of the background to the situation by independent procurement expert John McClelland has been commissioned on behalf of the council so that lessons may be learned for future projects.
“The results of this review will be brought to the council’s policy and resources committee as soon as practically possible.”
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