The newborn baby found abandoned last Friday has been named Maria and is doing well.
The infant, no more than a day and a half old when discovered, was left wrapped in a fleece blanket, inside a black bin liner and a paper carrier bag on a side road near farmland near the Dublin-Kildare border.
Gardai renewed their appeal for the mother to come forward and told her she has nothing to fear.
Officers said their main concern was for her safety and welfare and assured her they only want to reunite her with her baby, who is being cared for in the Coombe Women and Infants University Hospital in Dublin.
They displayed items that were found with Baby Maria by a passer-by on Friday afternoon at a farm gate on Steelstown Lane, Rathcoole.
They included a light brown throw made from fleece material and sold in Primark Home, a black refuse bag and a green paper carrier bag from Marks and Spencer which the infant was found in. A small blue cloth was also in the bag.
Baby Maria was just 24-36 hours old when she was found at the gate on Friday at about 3.30pm.
She had been wrapped in the fleece blanket in the bag by a man who had stopped his car.
There had been heavy and persistent rain in the area on the day but the baby was described as being fed and nourished when found and was in a stable condition when brought to hospital.
Officers involved in trying to trace the mother said Maria is now doing well and still in a stable condition.