The UK has only 24 Government departments.
The First Minister said the idea Scotland would need seven-and-a-half times as many departments as the UK was either a "horrendous blunder" or dishonest, and fatally undermined this week's Treasury paper on the costs of independence.
Published on Wednesday, the Treasury describes the paper as "the most comprehensive piece of work to look at the impact of independence on Scotland's finances" and say it "marks a major milestone in the independence debate".
It covers the initial financial position of an independent Scotland, start-up costs, growth, borrowing, SNP policy commitments, declining oil revenue and Scotland's ageing population.
The claim about departments was contained in a PowerPoint briefing given to the media ahead of publication which was titled "HM Treasury Scotland Analysis slides 230514".
One slide, titled "The costs of creating a new state", said: "The Institute for Government (IfG) and the London School of Economics (LSE) have published independent analysis which puts the average cost of setting up a new policy department at £15 million.
"Applying this to the 180 departments the Scottish Government states it would need could see Scottish taxpayers fork out £2.7bn."
However, the £15m figure refers to the start up costs of major Whitehall departments such as the Department of Energy & Climate Change or the Department for Work and Pensions, involving around 130 civil servants producing detailed policy work for ministers.
The Scottish Government has never said it would set up 180 ministerial departments.
Its White Paper refers to Scotland having 180 "public bodies", which are entirely different, and many of which are already well established.
These include large organisations such as NHS boards, Scottish Water and Scottish Enterprise, but also small quangos such as Quality Meat Scotland and the Cairngorms National Park.
The Scottish Government says much of the departmental infrastructure needed by an independent Scotland exists already, and so would not have to be built from scratch.
Coalition sources last night blamed a drafting error for the figure, but insisted the final analysis paper would accurately show the major start-up costs facing an independent Scotland.
Salmond said: "The Treasury's analysis is deeply flawed and deeply misleading, given their ridiculous claim that an independent Scotland would need 180 Government departments. The Treasury are either guilty of a horrendous blunder or it is a deliberate and deeply dishonest attempt to deceive - either way it leaves the Treasury's analysis without a shred of credibility, and either way they should withdraw this misleading claim."
The Treasury's mistake is a gift to the Scottish Government as it tries to downplay other aspects of Wednesday's analysis.
The paper is expected to pour cold water on the SNP's plan for a national savings fund using revenue from North Sea oil, arguing Scotland would have to borrow the money for such a fund, as it would be running a deficit and oil revenues would be in long-term decline.
Former Chancellor Alistair Darling, chair of the Better Together campaign, yesterday said that would be "ridiculous" and likened it to borrowing money on a credit card at high interest in order to save it at low interest.
"The crisis, the spending crisis, would hit Scotland on independence day," he said, adding the SNP would "say whatever it takes to try and win this referendum" regardless of the facts.
To offset the Treasury paper, Salmond will publish his own economic paper on Wednesday.
This will claim Scotland could "potentially" start saving money in a long-term oil fund on day one of independence in March 2016.
However, the SNP Government last night refused to give a commitment on starting an oil fund immediately, or to say what criteria would be used to determine the level of savings.
Norway has an oil fund worth £500bn, but this was based on saving when the country had a budget surplus, something Scotland has only achieved in a single year since 1991.
The SNP Government's paper will also update its projections for North Sea oil revenue.
These are expected to show a drop in revenue compared to figures issued in March 2013, a point the Unionists will use to claim the SNP's figures on independence cannot be trusted.
In response to Salmond's demand for withdrawal of the 180 departments claim, a UK Government spokesman said: "This is an own-goal by the Scottish Government. Their own White Paper says an independent Scotland will need 180 public bodies. The analysis simply reflects that."
Yes Scotland chair Dennis Canavan yesterday urged Darling to explain his recent meetings with Treasury mandarin Sir Nicholas Macpherson, who advised the Chancellor to reject sharing the pound with an independent Scotland.