They said that they are aware of three incidents where young girls were approached by a man who was 'possibly acting suspiciously'.
Two of the incidents involved girls aged 16, and the third involved a 15-year-old girl. They happened on 30 September, 13 October and 11 November.
Gardaí have issued a description of a man. They said he is black, with short hair or possibly a shaved head, and a distinctive yellow tooth.
He was driving a small red car. No age has been given for him. The gardaí say they wish to speak to him.
The statement was issued following a decision by a school principal in Skerries to inform parents about an attempted child abduction at a housing estate in the town last weekend.
The Minister for Justice, Michael McDowell said it was important sometimes not to draw too much attention to such cases.
However, Mr McDowell also said that the principal had acted very responsibly in issuing the letter.
Parents of pupils at St Patrick's Senior School were informed by the school yesterday that a number of attempts to take children had occurred in the area.
In a letter, the school principal, Michelle Keane, urged parents and children to be vigilant.
Ms Keane said a group of concerned parents had recently informed her about an attempt to coax a child into a car at a housing estate in the town last weekend.
The letter said the attempt had been unsuccessful, but that the gardaí were aware of a number of similar incidents, and had requested that any further occurrences be brought to their attention immediately.
The letter also urged parents and children to be vigilant. The principal said it was her belief and that of the board of management that parents need to be informed about this.
She said class teachers would be re-visiting relevant sections of the Stay Safe programme for pupils.
The letter was sent to parents by post as school management regarded it as 'inappropriate to disseminate through the children' because of what it described as the sensitive nature of the information.
