The demand by Holyrood’s Education Committee will put further pressure on the First Minister after he demoted Hyslop to culture and external affairs following her threat to take schools out of local authority control.
Labour MSP Hugh Henry’s call was immediately backed by the Conservatives and could be discussed by the committee on Wednesday - where its three SNPs are outnumbered by three Labour, one Tory and one Liberal Democrat.
In a letter to the convenor and fellow Labour MSP Karen Whitefield, Mr Henry, a former education minister in the last administration, said Mr Salmond had told him two years ago that a pledge to cut class sizes would happen during the Parliament’s lifetime.
He added: "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 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."
Liberal Democrat education spokeswoman Margaret Smith called for Mr Salmond to make a statement to Holyrood.
She said: "We've serious concerns that the SNP Government has broken three of their own codes of conduct during the class-size furore," she said.
"Over the weekend we had the third excuse for this shambles.
"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."
Last week 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.
Senior civil servant Donald Henderson had previously told an academic audience the scale of the task was too big to be delivered over a single parliament.
Salmond aides said the First Minister had not been made aware of the advice which was intended for the then Education Secretary Fiona Hyslopand the Scottish Government concordat deal with councils made clear the ambition to make "year-on-year" progress towards the class size reduction pledge.
A spokesman for Mr Salmond described Mr Henry's move as a "desperate effort" to divert attention.
"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," said the spokesman.
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