Fife Council has called in a decision to continue primary one testing at the request of Labour, Conservative and Lib Dem councillors.
The matter will be considered by a scrutiny committee and could be referred back to full council.
At a full Fife Council meeting in October, elected members were 38 votes to 27 in favour of asking the government to withdraw Scottish National Standardised Assessments (SNSA), amid claims they had left young children “distressed”.
But at a recent meeting of the council’s education committee, which was supposed to have the final say, a SNP-led bid to continue with the tests was passed by just one vote.
Conservative councillor Richard Watt said the decision was “undemocratic and in breach of Fife Council rules”.
Mr Watt condemned the decision as “anti-democratic trickery”, stating three unelected members representing churches and other religions had helped the SNP win the vote.
“Fife SNP played fast and loose with the council’s standing orders in the education committee which it convenes,” said Mr Watt.
“Fife SNP also had to rely on the votes of unelected religious representatives, whose membership in the past it has strongly objected to as undemocratic.
“It cannot be right that three unelected individuals can just reverse a carefully considered decision made by 75 elected members of Fife Council at the behest of SNP councillors whose priority is shoring up the SNP government at Holyrood.”
Opponents of SNSA say the tests are not in line with the recommended model of play-based learning for very young pupils.
At Holyrood, MSPs voted by 63 to 61 to pass a Conservative motion calling for a halt to the tests.
Council manager for committee services Andrew Ferguson said: “I confirm a valid call in of the decision has been received.
“In line with standing orders, this will be put to the next scrutiny committee on December 4.
“The scrutiny committee will then review the decision taken at education and children’s services committee.
“If scrutiny agrees with the original decision it can go ahead. If it disagrees, then the matter will be referred to full council for a final decision.”
The education committee’s SNP convener Fay Sinclair said: “The council motion said the assessments should be withdrawn ‘if possible’.
“Legal advice was that such a withdrawal would have to be evidenced as ‘reasonable and proportionate’ and the education committee did not believe this legal requirement was met.”