Gardaí have noticed an increase in the number of reported attempted abductions since the kidnapping and murder of Holly Wells and Jessica Chapman in Britain last month.
A Garda spokesman said many of these turned out to be innocent cases where a car may have broken down or someone may have been genuinely seeking directions.
However, he said, gardaí always encouraged people to be on the alert and to report any suspicious incidents, no matter how trivial. "We don't mind if it turns out to be a false alarm," he said.
There have been a number of reported abduction attempts in the north-east in recent months. One of the most publicised occurred just three days after Holly Wells and Jessica Chapman went missing.
On August 7th Kelly Mullen (9) and Ciara Brady (10) were playing football close to their homes at Cox's Demesne in Dundalk when a white Northern Ireland-registered Toyota Corolla stopped beside them.
The driver first asked directions from the girls but then returned and asked for more directions and said he would give them €10 if they would get into the car with him.
About 90 minutes later a man with a similar description pulled up alongside a 12-year-old girl in another estate in Cox's Demesne. The man drove off when she was called by her brother.
Similar approaches were made to young girls in the same part of Dundalk in March and July.
Meanwhile, on August 14th, three teenage girls were walking home between Bray and Shankill, Co Dublin, when a man driving a gold-coloured Fiat Punto pulled up beside them. He gestured for the three to get into the car and as they backed away he patted the passenger seat and waved a €10 note at them.
Later that month a man was badly beaten in the Moyross area of Limerick after parents claimed he had tried to lure children into his car. Gardaí stressed that no children had been touched or harmed. The man was questioned and a file sent to the DPP.
Meanwhile, in June a 34-year-old Co Offaly man appeared before Mullingar District Court on charges regarding the abduction and sexual assault of a 10-year-old girl at Kilbeggan earlier that month. He was remanded in custody.
A Garda spokesman said parents should always know where their children are and who they are with. Even at home, parents should not let their children out of their sight. "It only takes a few seconds for children to wander off."
Gardaí have also advised parents never to allow their children to play outdoors late in the evening or at night. When older children go out at night, parents should know where they are going, and if they are carrying mobiles phones they should ring them occasionally to check on their whereabouts.
The National Parents' Council (Primary) has advised parents to ensure that their children are always supervised when outdoors.
However, Ms Fionnuala Kilfeather, NPC chief executive, said it was also very important to use common sense and not to terrify children.
She said she had heard reports of parents in Britain refusing to allow children outdoors at all, and said such children would not grow up to be normal, well-adjusted adults.
"Children have to be taught gradually to take more responsibility for themselves. It should be done in a low-key way," she said.
Ms Kilfeather said there should also be more of a community attitude in neighbourhoods, with people looking out for the children of others.
"Make sure you keep lines of communication open with children so you can discuss difficult topics like these," she said.