The body representing the parents of primary school pupils has called on the teaching unions to adopt an "open-minded" stance on the move to make compulsory testing a requirement in all primary schools.
After the main primary teaching union, the INTO, said it would oppose the measure, the National Parents' Council Primary said there was a responsibility on all in education to be open to such testing.
"Information is a valuable resource, and the real debate should be around how the information is used in the best interests of children," said the council's chief executive, Ms Fionnuala Kilfeather.
In what she described as a "cautious welcome" to the initiative, Ms Kilfeather said a systematic approach to assessment was essential to monitor the progress of individual children.
Asked why the teaching unions were opposing the measure, she suggested that there may be a fear that the system would be used to identify under-performing teachers.
However, the INTO said the assessment method proposed by the Minister for Education, Mr Dempsey, was discredited, and had failed in other countries.
"It is hard to believe that anyone would want to import such a discredited way of testing children into Irish primary schools," said the union's general secretary, Mr John Carr.
Criticising Mr Dempsey for not consulting with the teacher unions, he said the measure would damage the primary school curriculum.
"From 1942 to 1967, every child in sixth class in a primary school had to sit the Primary Certificate.
"The examination led to feelings of inferiority and failure among young children. It had no practical value, and skewed the purposes of education. It made no allowance for special needs."
The education research officer of the Teachers' Union of Ireland, Mr John MacGabhan, said the announcement had come at a peculiar time.
"We are surprised and disappointed at the absence of consultation on matters that are clearly significant.
"In terms of the particular proposals, we will operate as we have done, through our representatives on the National Council for Curriculum Assessment."
Fine Gael's education spokeswoman, Ms Olywn Enright, said standardised testing should give an objective overview of literacy and numeracy standards.
However, such a system should be managed in a manner that was sensitive to the young age of the children being tested.
"The introduction of such a system requires the utmost care and sensitivity, and I have concerns that seven may be too young an age for tests of this type. When dealing with children at primary level, we must make sure that any future tests do not promote stress or anxiety."
Labour's spokeswoman Ms Jan O'Sullivan accused Mr Dempsey of going on a "solo-run" without consulting teachers or parents.
"He must clarify the exact purpose of these tests. Are they merely an information-gathering exercise? Or will he subsequently commit to provide sufficient resources to help those children who are found to have below-average levels of numeracy and literacy after they have sat the tests?"
