The government has "no plans" to bring in new laws governing when a women can legally have an abortion, Prime Minister David Cameron has said.
The PM spoke after Health Secretary Jeremy Hunt told the Times he personally favoured a move to halve the abortion limit from 24 weeks to 12.
Mr Cameron said Mr Hunt was "entitled to hold an individual view" but insisted it was not government policy.
The 24-week limit applies to England, Wales and Scotland.
Abortion is illegal in Northern Ireland except in exceptional medical circumstances, such as when the mother's health is at risk.
During a visit to the John Radcliffe hospital in Oxford, Mr Cameron said he "personally" favoured a "modest reduction" from the current limit of 24 weeks, "because I think there are some medical arguments for that". But he said he did not agree with the 12-week limit.
Mr Hunt told the paper: "My view is that 12 weeks is the right point for it."
The health secretary said he had reached the conclusion after studying the evidence, adding it was his personal view over what remains an "incredibly difficult question".
Responding to his comments, Home Secretary Theresa May told the BBC she "probably" backed a change to a 20-week limit but also said that that was a personal view.
Earlier this week Women's Minister Maria Miller told the Daily Telegraph she would vote to lower the abortion limit from 24 weeks to 20 weeks.
Tory MP Daniel Kawczynski, who wants the existing law tightened, welcomed Mr Hunt's comments.
"The health secretary coming out in favour of reigniting this debate will galvanise the caucus that exists in Parliament, cross-party, on this issue," he said.
But Anthony Ozimic, from anti-abortion campaigners the Society for the Protection of Unborn Children, said that any new backbench bill on the topic was certain to fail.
"There is a large pro-abortion majority in Parliament which will ensure that any time-limiting amendments are rejected while using the opportunity to push for pro-abortion amendments," he said.
"The real political debate about abortion in the UK should focus... on the right to life of all unborn children and on the way governments bankroll abortion access at home and abroad," Mr Ozimic added.
Shadow home secretary Yvette Cooper, who speaks for Labour on women's issues, said the statements by Mr Hunt "show the health secretary has given no serious consideration to women's health".
She added: "Perhaps the most chilling part of his interview is the claim that 12 weeks is based on evidence when it undoubtedly is not."
Gynaecologist Professor Wendy Savage, a campaigner on women's rights, expressed concern over the possible re-opening of a debate which was defeated the last time it came to Parliament in 2008.
She said: "The number of abortions that take place over 20 weeks is very small. Of those a considerable proportion are of foetuses which have got a congenital abnormality.
"I think the majority of the population think that if somebody has got a foetus that, if born, will have a severe disability they should have the right to choose whether or not to continue with that pregnancy," she said.
Prof Savage added that ministers should be debating whether to decriminalise abortion altogether.
Elsewhere, the British Pregnancy Advisory Service's Clare Murphy said the remarks reflected "a lack of understanding of why women need later services".
There were nearly 190,000 abortions for women in England and Wales last year, 91% of which were carried out before the 13th week of pregnancy, according to Department of Health figures.