David Cameron has backed calls to reduce the time limit for abortions by as much as a month.
The Conservative leader said he would like to cut the current time limit from 24 weeks, citing evidence of improved survival rates for babies born very prematurely.
The statement follows the Conservatives' new policy strategy on women, which made no mention of reproductive rights.
Anti-abortion MPs are set to use the human fertilisation and embryology bill to introduce amendments restricting women's access to abortion, including reducing the legal time limit for abortion to 20 or 21 weeks.
The current 24-week limit was passed in 1990 after MPs amended the original 28-week limit in the light of medical advances since the 1967 act was passed. Abortion can be legally carried out beyond this limit if there is a risk of serious disability.
Mr Cameron was quoted by the Daily Mail as saying he would like to a see a further reduction in the current limit.
"It is clear that, due to medical advancement, many babies are surviving at 24 weeks," he said.
The Tory leader added: "If there is an opportunity in the human fertilisation and embryology bill, I will be voting to bring this limit down from 24 weeks.
"This must, however, remain a conscience issue and a free vote."
The government has no plans to amend the Abortion Act but MPs from all parties are expected to be granted a free vote on contentious issues in the forthcoming bill.
Downing Street today confirmed Gordon Brown does not believe there is any reason to change the law.
The prime minister's official spokesman (PMOS) said he had "always made clear that he thinks we should be guided by the best medical advice on this".
The PMOS added: "At the moment, the key organisations in the medical profession are not pressing for a review in this area.
"For example, both the British Medical Association and the Royal College of Obstetricians and Gynaecologists have said they do not believe there is a case for changing the time limits for abortion."
The Commons science and technology committee last year rejected calls to reduce the time limit, while also arguing access to early abortion should be improved.
Abortion rights campaigners argue women most affected by a ban on later-term abortions would be the very young and pre-menopausal.
Liz Davies, director of UK and western Europe operations at Marie Stopes International, said: "We must recognise that there will always be a need for later terminations, as a proportion of women, through no fault of their own, either do not recognise symptoms of pregnancy or have no reason to suspect that they could possibly be pregnant at all if, for example, they are regularly using a modern form of contraception."
The Pro-Life Alliance does not explicitly support attempts to reduce the abortion time limit as it works instead to restrict all abortion.