The baby girl, who is pictured, was found in a box outside a house in Ibsen Walk, Corby, on Monday morning. It is believed she could have been left outside the property as early as 6am.
Today, Detective Superintendent Steve Lingley appealed to the baby's mother to contact him so he could be sure she is safe.
He said: "I want to appeal directly to the mother of the little baby who was found outside a house in Corby on Monday. Your baby is safe and is being well cared for.
"I know you may feel you are in a very difficult position and I know it must have been incredibly difficult to have left your baby.
"But please get in touch with us - we want to make sure you are alright."
This baby girl is three to six weeks old.
She was found wrapped in a blanket wearing just a nappy and has dark hair and dark eyes.
The mother, or anyone who has any information about her or the baby, can contact the police by calling 101.
Alternatively, they can call the independent charity Crimestoppers anonymously on 0800 555 111 or use the anonymous online form at www.crimestoppers-uk.org.