Kfm News understands that one parent impacted received a letter this morning confirming a school place for her son.
Around 30 children in Naas are still without a confirmed school place for September.
Independent Ireland councillor Bill Clear says families are facing unnecessary stress and uncertainty as a result, describing the situation as a failure of forward planning by the Department of Education.
He said the town’s rapid population growth and ongoing housing development have not been matched by sufficient school capacity.
Councillor Clear has urged the Department to outline what steps will be taken to ensure every child in Naas has a place for the new school year.
He said such a situation did not happen in the 1950s, 60s or 70s, 80s when the country was "far poorer" than it is now.
One parent affected is Lucy Stokes, who had been unable to secure a place in any of the six Naas schools she applied to for her four-year-old son, Edward, known as Teddy.
Kfm News understands, however, that Ms Stokes received a letter this morning confirming a school place for her son.

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