The demand for a probe by Holyrood’s Education Committee came from Labour’s Hugh Henry and was immediately backed by the Tories.
The call could be discussed at tomorrow’s meeting of the committee, whose three SNP MSPs are outnumbered by three Labour MSPs, one Conservative and one LibDem.
Mr Henry’s call for the inquiry was made in a letter to the committee’s Labour convener Karen Whitefield.
Mr Henry, who was an education minister in the previous Labour-LibDem administration, said Mr Salmond had told him in 2007 that a pledge to cut class sizes would happen in the lifetime of this Parliament.
Mr Henry went on: “We know that ministers were told that the pledge was undeliverable, we know that the then Education Secretary Fiona Hyslop knew it was undeliverable, but we are asked to believe that Alex Salmond was never told. This inquiry needs to establish who was told what and when.
“It also needs to establish whether this policy could have been implemented by 2011, as promised by the First Minister in September 2007.”
Deputy Tory leader Murdo Fraser said: “Many people will find it difficult to believe that Alex Salmond was unaware that his own senior education advisers had made it clear the SNP’s flagship class-size pledge could not be delivered in the lifetime of this Parliament.
“Instead of hanging his former education secretary out to dry, Alex Salmond should come clean, and this inquiry is the ideal place to do just that.”
Meanwhile Liberal Democrat education spokeswoman Margaret Smith called for Mr Salmond to make a statement to Parliament.
“We’ve serious concerns that the SNP Government has broken three of their own codes of conduct during the class-size furore,” she said.
“The only way that this mess can be cleared up is by a statement from the First Minister to the Parliament as soon as possible.”
The row erupted on Thursday, when Labour accused the First Minister of misleading Parliament in September 2007 by saying a pledge to cut class sizes to 18 for primary 1-3 would be delivered in the lifetime of this Parliament.
Two months previously, senior civil servant Donald Henderson had told an academic audience that this would not be possible.
Salmond aides said the First Minister had not been made aware of the advice, which was intended for the then Education Secretary Fiona Hyslop, and that the concordat deal with councils made clear the ambition to make “year-on-year” progress towards the pledge.
A spokesman for Mr Salmond described Mr Henry’s move as a “desperate effort” to divert attention.
He said: “The document has been in the public domain for nearly two years and repeatedly raised in Parliament, and Hugh Henry keeps shifting position on what he is calling for from one day to the next.”
Last week Mr Salmond’s own team of high-level advisers, the Scottish Government’s Council of Economic Advisers, questioned the Scottish government’s drive towards reducing class sizes, claiming it had evidence the flagship policy had “a limited impact”.
The report said: “The council is sceptical that the simple objective of reducing class size, as a method of improving teaching, will prove sufficient.”
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