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. The issue is one reserved to Westminster which Holyrood has no control over.
Earlier, the new Health Secretary Jeremy Hunt said he believed the limit should be cut to 12 weeks, though he claimed his view weren't influenced by his Christian faith.
Culture Secretary Maria Miller, who is also the Minister for Women, has also said that she would like a 20-week limit, raising fears that there might be a new push forthcoming in Parliament to change the law.
The comments have horrified women's rights activists, who warned that a reduction to 12 weeks could effectively prevent testing for conditions such as Down's syndrome.
There were around 200,000 abortions in the UK last year. The vast majority – 91% – were carried out under 13 weeks into pregnancy.
Shadow home secretary Yvette Cooper, who speaks for Labour on women's issues, described Hunt's remarks as "chilling".
She said: "Jeremy Hunt's statements on abortion are deeply worrying and show the Health Secretary has given no serious consideration to women's health."
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. But she said: "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."
The intervention of Hunt, who was moved to the health brief in last month's Cabinet reshuffle, has galvanised anti-abortion campaigners.
Hunt said: "My view is that 12 weeks is the right point for it. It is just my view about that incredibly difficult question about the moment that we should deem life to start. I don't think the reason I have that view is for religious reasons."
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 said. "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."
Diane Abbott, Labour's public health spokeswoman, said: "We're seeing a sustained ideological attack on the science, and the rights that British women and families have fought for. There is no evidence to support a reduction in the abortion time limit and this view is supported across the medical profession."
David Cameron said he did not agree with Hunt's position, but the minister was entitled to his opinion. The Prime Minister added: "People need to know the Government has got no plans to bring forward any legislation in this area."
Darinka Aleksic, campaign co-ordinator at pressure group Abortion Rights, said it was "absolutely outrageous" that the Health Secretary wants to "radically restrict access to those services".
"Abortion is an absolutely key part of women's healthcare. Clearly he [Hunt] hasn't looked at the scientific evidence around this at all because there's no medical basis for reducing the abortion time limit."
Clare Murphy, of the British Pregnancy Advisory Service, said: "Politicians are absolutely entitled to their own personal convictions, but I do think it's different when a health secretary makes so public his position on this; a health secretary who is responsible for services for millions of women across the country. I do think it reflects a lack of understanding of why women need later [abortion] services."