Tory MP Nadine Dorries has said she will publish a new version of her bill to reduce the time limit for abortions.
More than 186,000 abortions were carried out last year
The new version would limit the timescale for terminations to 20 weeks from the current 24 weeks.
Ms Dorries' previous proposals to cut the maximum period to 21 weeks were rejected by MPs in October.
She said her aim was to cut the number of "barbaric" terminations involving lethal injections. Opponents say the plans limit women's freedom.
The new bill - to be republished on Monday - calls for a one-week "cooling-off" period between a request for an abortion and it being performed, to provide time for counselling.
The previous bill stipulated a 10-day period.
Labour MP Chris McCafferty has called the cooling-off proposal "an attack on women's reproductive rights".
The previous bill submitted by Ms Dorries - MP for Mid Bedfordshire - failed by 187 votes to 108 in the Commons.
Announcing the publication of the new version, she said: "Many people are not aware that in order for a late abortion to take place for social reasons, foeticide must first take place; this process can take up to two days and involves a lethal injection being administered into the foetal heart via a cannular through the mother's abdominal wall.
"When a doctor is sure the foetal heart has stopped, the dead foetus is delivered on day two using forceps.
"Clearly this is a barbaric practice and I will not stop campaigning until it is outlawed.
"How can it possibly be right that on one hospital ward we have doctors working to save the life of a baby born at 22 weeks, yet on another a doctor is aborting one of the same gestation?"
She said that she hoped the bill would remain on the list of pending parliamentary business until the 40th anniversary next year of the 1967 Abortion Act, which legalised the termination of foetuses up to the 24th week of pregnancy.
All the main parties consider the issue of abortion, of which there were 186,400 in England and Wales last year, to be one on which individual MPs should have a free vote, rather than following a party line.
Department of Health statistics show that 89% of abortions in 2005 were carried out before the woman was 13 weeks pregnant, with 67% performed at under 10 weeks.
Ms McCafferty has said that forcing a woman to have counselling goes against the whole principle of counselling, while the 10-day delay could prompt women to travel abroad for abortions "when they are in a vulnerable state" or resort to illegal abortions.