Campaigners have vowed 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 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 present maximum.
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.
However the move horrified women's rights activists who warned that a reduction could effectively prevent testing for conditions such as Down's syndrome.
Mrs 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. But 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." she told the BBC Radio 4 Today programme.
But 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.
"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."