Seventy two per cent of those questioned in the ComRes poll for the Christian campaign group, CARE said they supported the existing laws which require the signatures of two doctors before an abortion can be approved.
It comes as MPs debate relaxing the restrictions to make abortion more freely available.
Last month marked the 50th anniversary since the 1967 Abortion Act, with almost 9 million abortions taken place since it was introduced in Great Britain.
The polling highlights only 8 per cent thought abortion should be allowed if a woman feels her family is big enough and just 4 per cent if a woman feels that continuing with the pregnancy would get in the way of an educational or employment opportunity.
Only 12 per cent of people thought it should be legal to terminate an unborn child with Downs Syndrome which is currently legal up till birth. Preventing abortion in these contexts would require a tightening of the law.
The Christian campaign group, CARE's Chief Executive, Nola Leach told Premier that MPs should take notice of the poll and the views of the public.
She said: "My message and CARE's message to MPs talking about this issue is, get your facts right, get the information from women who have actually been through these experiences and know that it is a very painful decision that they weren't perhaps given the time and the space to make their decision."
She went on to say there is clearly still a mainstream view in society that abortion needs to be governed within a legal framework. This ensures protection for the woman, having two doctors sign off on an abortion is a vital safeguard which helps make sure the woman is not being coerced into having an abortion and has plenty of one-to-one time with a medical professional to discuss her concerns.
She added: "Rather than making abortion more widely available we should be doing more to support women and children in pregnancy and beyond for the good of our society.
"Time would be better spent in parliament debating cutting the time limit of abortion down from 24 weeks, in line with public opinion. The 24-week limit is becoming increasingly out of touch with medical and technological advances as more babies born before this limit are surviving."