A Labour MP has called for the present 24-week mark after which abortions become illegal to be shortened ahead of a meeting between the health secretary, Patricia Hewitt, and Cardinal Cormac Murphy O'Connor next week.
Geraldine Smith MP hopes to revive the debate around an issue which is highly divisive in the United States but largely settled in Britain.
Ms Smith has also tabled a Commons motion calling on the government to create a committee of MPs and peers to debate the issue.
The Morecambe and Lunesdale MP was one of those behind a report last year calling for a fresh look at the law in the light of new medical technologies.
A poll earlier this year found that the majority of women in Britain want the law tightened to make it harder to terminate a pregnancy.
Cutting the time limit was backed by 47% of women and another 10% were opposed to abortion under any circumstances - with just 2% backing later abortions. But doctors have voted against calls for a new 20-week limit to recognise the medical advances which allow very premature babies to survive.
Ms Smith said: "What I find is that even women with a very strong pro-choice view do recognise that the time limits should be reviewed.
"I think people's opinions are beginning to change on this issue as technology means babies born earlier can now be kept alive. What we really need is a public debate and a debate led by Parliament."
She added: "I think there probably needs to be a reduction in the time limits. You have to look at why these late abortions are happening." Her motion has been signed by another seven MPs, including Ian Gibson, Labour MP for Norwich North, who chaired the science and technology committee which called for a debate last year.
It calls for consideration of "the scientific, medical and social changes in relation to abortion" since the law was first introduced 40 years ago.
Next week the leader of the Catholic Church in England and Wales, Cardinal Cormac Murphy O'Connor, is due to hold talks with Ms Hewitt to demand changes to the law and practice of abortion in Britain.
