The education secretary has been criticised by a statistics watchdog for claiming that one in three pupils left primary school unable to read or write under Labour.
UK Statistics Authority chairman Sir Andrew Dilnot told Nicky Morgan she should "reconsider" her comments.
He said she might need to correct the parliamentary record.
It was the second time Sir Andrew has rebuked ministers over the claim, based on 11-year-olds' national test results.
On December 10 in the Commons, Ms Morgan told the shadow education secretary, Tristram Hunt, "he ought to be thinking about the fact that under the previous Labour government one in three of our young people were leaving primary school unable to read and write".
She added that it was a "shocking statistic".
In tests taken in England in May 2010, 83% of pupils were assessed at Key Stage 2 as reaching at least level four - the expected level at age 11 - in reading, 71% in writing, and 79% in mathematics.
Mrs Morgan's claim, which was made in the House of Commons, was apparently based on figures showing 64% of pupils in England achieved level four or above in all three of reading, writing and maths.
But referring to the published definitions of the levels, Sir Andrew said children who reached Level 3 were able to "read a range of texts fluently and accurately".
They are also able to write in a way that is "often organised, imaginative and clear" and they can "add and subtract numbers with two digits mentally and numbers with three digits using written methods".
He added that in tests taken in May 2010, 91% of pupils were assessed as reaching level three or above at Key Stage 2 in reading, 93% in writing, and 93% in mathematics.
Sir Andrew told the education secretary: "I think that it would be appropriate for you to reconsider these comments. You may also wish to take advice on whether the official parliamentary record should be corrected."
Ms Morgan's comments came less than a week after Sir Andrew had criticised the use of the statistic, included in speeches to the Conservative Party conference.