Campaigners vowed on Saturday to re-open the fight to tighten up the abortion laws after a third Cabinet minister came out in favour of cutting the current 24-week limit.
Home Secretary Theresa May has said she believed there was scope to reduce the limit on when a termination can take place, to 20 weeks into a pregnancy.
Earlier the new Health Secretary Jeremy Hunt went even further, saying he believed the limit should be cut to 12 weeks - half the current maximum of 24 weeks.
With Culture Secretary Maria Miller, who is also the minister for women, having already said that she would like a 20 week limit, campaigners signalled a new push in Parliament to change the law.
Theresa May became the third government minister to express her belief in lowering abortion limits
However, May stressed that all the ministers concerned were expressing personal views and that the Government had no plans to review the 24-week time limit.
"The Government has no plans to change the law on this, we have got no plans to reduce the abortion limit," she told the BBC Radio 4 Today programme.
She added, however: "I think there is scope for some reduction. My own view is probably a reduction to 20 weeks. That is a personal view of mine."
Leading Labour figures such as shadow home secretary Yvette Cooper, who speaks for Labour on women's issues, described Hunt's remarks as "chilling".
Jeremy Hunt, the newly-appointed health secretary, expressed his belief in a 12-week limit
"Jeremy Hunt's statements on abortion are deeply worrying and show the Health Secretary has given no serious consideration to women's health," she said.
Shadow public health minister Diane Abbott has also criticised the Tory ministers coming out in favour of cutting the limit.
In an exclusive blog for the Huffington Post UK, Abbott claimed "their opinions on the time limits for abortions obviously have no basis in medical fact. The people best placed to know whether there is any scientific case for lowering time limits are doctors, specifically doctors that specialise in women and childbirth."
Professor Wendy Savage, a gynaecologist and campaigner on women's rights, expressed alarm at the prospect of another move to reduce the limit following the defeat in Parliament of the last attempt in 2008.
Diane Abbott strongly criticised Jeremy Hunt's position on abortion
"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," she told Today.
"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."
Tory MP Mark Pritchard, the vice chairman of the parliamentary pro-life group, said that it was time for an "up-to-date" national debate on the term limits for abortions.
"The law currently lags behind recent scientific breakthroughs, where the survivability of young babies has increased greatly. It is time for the Government to make time for a full debate on the issue," he said.
"It is a tragic irony that at one end of a hospital taxpayers are paying for the termination of babies, whilst at the other end of the same hospital, taxpayers are paying to create babies through IVF."