The provision of nursery places was an executive pledge
Education Minister Cathy Jamieson has denied that 9,000 pre-school children are failing to get access to free nursery places.
It follows a warning that Scottish councils may face legal action over the provision of pre-school education.
Mrs Jamieson refuted the claims and said that the Convention of Scottish Local Authorities (Cosla) had also refuted them.
From April last year every local council has had a duty to provide free nursery school places for every three and four-year-old child.
The Scottish Executive has hailed delivery of the provision as one of its key policy successes.
However, it has been reported that a test case on behalf of parents could go to the Court of Session.
I don't want to see any situation where a parent feels they have to go to court to get what is rightfully theirs
In Dunbar, East Lothian, a mother whose daughter reportedly failed to get a council-provided nursery place is considering legal action.
Mrs Jamieson said that 85% of three-year-olds and 96% of four-year-olds now has a place in nursery education.
She said many parents do not wish their three-year-olds to take up a place and she would investigate if any were being denied.
Mrs Jamieson told BBC Scotland: "We have made it a responsibility of the local authorities to secure nursery provision for all three and four-year-olds... and local authorities have also had the funding to deliver that.
"If that is not happening then I am very concerned about it and I will be making immediate inquiries to find out where the problem is and how that can be resolved.
Cathy Jamieson: "Concerned"
"I don't want to see any situation where a parent feels they have to go to court to get what is rightfully theirs, but we do need to ensure that this is resolved.
"I am aware that there has been a problem in a local authority area where some parents have not been able to access the provision of their first choice, but the claims that 9,000 young people are not getting the places are simply not accurate."
Scottish National Party education spokesman Mike Russell described the executive's delivery of nursery provision as "abysmal".
"The local authorities would argue that they are not funded properly to do this and have great difficulty in doing it.
"The executive's number one policy was to put this in place. They now say they have done it.
"We discover a week after they say they have done it that they have not done it.
"It is very serious for parents affected by this and their approach to this and other delivery matters is frankly abysmal."