Concerned officers said all they wanted was for her to come forward and avail of any medical or psychological help she might need.
The body of the full-term baby girl was found abandoned in a holdall bag near Sandymount beach, near Ringsend, Dublin, on Sunday night.
"Our main concern is to get this woman identified, get her medical treatment and anything else can be dealt with down the road," said Supt Jerry Philips of Donnybrook Garda Station.
"She need have no fear of the gardaí. All we're trying to do is assist her at the moment and get her medical attention as soon as possible. She will be treated very sensitively and in the strictest confidence."
A postmortem carried out on the child showed that there was no physical injuries or any evidence of foul-play.
Crisis pregnancy agencies yesterday expressed concern at the physical and mental pain the distressed mother might be suffering.
"Clearly any woman who's gone through what this woman has gone through needs to be dealt with very sensitively. She had nowhere to turn to and is now faced with a very distressing situation," said Karen Kiernan, manager of pregnancy counselling service Cherish.
"I'd like to express my deep sympathy to her and her predicament. I would urge her to seek help and confide in somebody she trusts. She may be at a very difficult juncture herself."
A spokeswoman for the Irish Family Planning Association (IFPA) said the case was not unusual. "Cases like this happen every single year. It's not something that goes away, or is out of the ordinary. Generally there are two cases each year and has been over the past 10-15 years." She said most women with a crisis pregnancy felt fear and isolation and experienced their pregnancy in secrecy.
Ms Kiernan said the woman may have abandoned her baby because she was in denial of her pregnancy.
"That could be to do with the family situation, her own circumstances or how the pregnancy took place. If she is very deeply in denial then other people could be in denial."
l Cherish can be contacted at 01-6629212. The IFPA can be contacted at 1850 495051.