The V&A Dundee is due to open in September but concerns have been raised over its financial sustainability.
During First Minister’s Questions at Holyrood, Labour MSP Jenny Marra told MSPs: “A board paper for V&A Dundee states that our new museum needs more cash to cover operating costs, a £500,000 bank loan and potentially further government grants.
“It is my understanding that costs have been under-estimated or missed and there is not a clear plan for where future revenue will come from to run the museum and to service the bank loan after the initial opening phase.”
She called for assurances from the Scottish Government that it was working to ensure the project is on a “firm financial footing”.
While the museum is not a Scottish Government-led project, ministers have provided £38 million towards construction and £5.5 million in revenue funding.
Nicola Sturgeon said: “We have also agreed a further package of revenue support that will be worth £1 million a year and support the museum in the first 10 years of its operation.
“The Scottish Government is committed to supporting this fantastic new development for Dundee.
“I think for many years, decades and generations to come this will be a new museum that people not just in Dundee, but right across Scotland, will be thoroughly and very rightly proud of.”
A V&A Dundee spokesman said the museum had arranged an overdraft facility, not a £500,000 loan.
“Every successful organisation plans for its finances, including assessing potential risks, and as part of that we have organised an overdraft as the museum prepares to open,” he said.
“We have not borrowed money - this option would only be used for cashflow purposes, not to run the museum.”
He added: “Thanks to the long-term support of our founding partners, private supporters and others, we are in a strong position to launch and run the new museum. We are very confident the museum will be an international success.”
He said the annual £1 million post-opening funding was agreed in 2014 and was not new money.