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The institution has a £30m blackhole in its finances and has been warning of job cuts including compulsory redundancies.
Lecturers and other staff began 15 days of strike action at the start of the week.
The Courier reported that the package will help the university bridge the gap while an action plan is put in place for a longer-term solution.
Announcing the loan, Ms Robison urged Labour’s finance spokesman Michael Marra, who represents north east Scotland, to support the Budget Bill.
“Dundee is watching,” she told him.
He welcomed the new funding but said there still needed to be a full rescue package for the institution.
“What we have here is an illustrative case of the SNP fixing one symptom of a much greater problem that it has helped to cause,” Mr Marra said.
News of the loan for Dundee came just hours after Edinburgh University’s principal announced plans to reduce staff numbers to plug their own £140m black hole.
University principal Professor Sir Peter Mathieson said “radical university-wide actions” were needed to make the savings, which will lead to “a smaller staff base and lower operating costs”.
Last week Professor Steve Oliver, the principal of Robert Gordon University (RGU) in Aberdeen, said Scotland’s universities are facing a “major existential threat” through being “significantly underfunded”.
The Lib Dems, Greens and Alba all gave the budget their backing after the parties secured a number of concessions from ministers.
With the Scottish Greens, the Scottish Government agreed a 12-month pilot for a £2 bus fare cap starting from 1 January 2026, and more money towards free school meals.
The deal with the Lib Dems saw increased investment in drugs and neonatal services for babies exposed to drugs in the womb, as well as an extra £1 million for hospices and more money for colleges.
Ms Robison told MSPs: “This is a budget delivering record NHS investment, record Local Government funding, £4.9 billion in climate positive investment, a universal winter fuel payment for the elderly, and the decisive steps necessary to effectively scrap the two-child benefit cap in 2026.
“Following spirited discussions, that whatever our other disagreements, the Scottish Green Party, Liberal Democrats, and Alba have indicated they can support this budget. I thank them for their pragmatic approach which sees this budget contributing towards their priorities.
“This is a budget to improve services, tackle child poverty, and bring new opportunities. It’s not enough to will the ends, you must will the means.”
Tory MSP Craig Hoy said the “dire budget” had passed “without even a flicker of opposition from the spineless Labour Party.”
He added: “The cosy, left-wing consensus at Holyrood has given us the UK’s highest taxes and a welfare bill and government spending that are no longer sustainable or affordable.”
Mr Marra pointed to the £5.2bn uplift to the block grant following Chancellor Rachel Reeves’ budget last year. He said the SNP plans were only possible “because the Labour UK government moved decisively to end austerity, rebuild the public finances and invest in public services.”
He added: “Labour delivered the largest budget settlement in the history of devolution, and the SNP lined up with the Tories to vote against it.
“We will not stand in the way of Labour’s record investment reaching the frontline of Scotland’s public services. After years of Tory austerity and SNP incompetence, a funding boost is badly needed.”
Meanwhile, councillors in Orkney voted narrowly in favour of a proposed 15% increase in the islands’ council tax – after rejecting a suggested rise of 20%.
That was despite Ms Robison saying last year that the £1bn uplift in funding for councils should mean local authorities did not need to introduce any “large” tax increases.
Falkirk Council could be about to increase its council tax by around 13.7% next week.