Conservative leader David Cameron has said that the time-limit for abortions should be cut to "20 or 22 weeks", in an interview with a Roman Catholic newspaper.
Mr Cameron backed a cut to 22 weeks in 2008, when the House of Commons voted to keep the existing maximum of 24 weeks.
But he indicated that he might be willing to go further when he told the Catholic Herald that a new review was now needed.
"My own view is that we do need to review the abortion limit. I think that the way medical science and technology have developed in the past few decades does mean that an upper limit of 20 or 22 weeks would be sensible," said Mr Cameron.
He indicated that Conservative MPs would be allowed a free vote on the question, as is normal with issues of conscience.
Mr Cameron also warned against legalising assisted suicide, saying: "My personal view is that if assisted dying is legalised, there is a danger that terminally ill people may feel pressurised into ending their lives if they feel they've become a burden on loved ones."