Conservative leader David Cameron has said he would back a cut in the legal time limit for abortion if MPs are given a chance to vote on the issue.
Mr Cameron said abortion must remain a "conscience issue" for MPs
It is expected MPs will seek a vote on cutting the 24-week limit - possibly to 20 weeks - in an amendment to the Human Fertilisation and Embryology Bill.
Mr Cameron told the Daily Mail he would "like to see a reduction", as survival rates after early births were rising.
The government said there were "no plans" to change abortion laws.
An amendment to the bill, currently going through Parliament, could provide the first opportunity for MPs to vote on the issue since 1990.
Abortion is an issue which is traditionally left as a free vote - MPs are not told to vote a certain way by party leaders.
Aides stressed that Mr Cameron was not seeking to pressure Tory MPs to follow him and vote for a reduction.
Mr Cameron told the Daily Mail: "I would like to see a reduction in the current limit, as it is clear that, due to medical advancement, many babies are surviving at 24 weeks.
"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."
Gordon Brown's official spokesman said the prime minister "has always made clear that he thinks we should be guided by the best medical advice on this.
"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 government has no plans to change the law on abortion."
No amendment has yet been tabled in the House of Commons proposing a particular reduction.
While debating the 1990 Human Fertilisation and Embryology Bill, MPs voted on options varying between 28 and 18 weeks, choosing the current 24-week limit.