Health Secretary Jeremy Hunt has said he would favour a change in the law to halve the limit on abortions from 24 weeks into a pregnancy to 12.
His comments to the Times came after Women's Minister Maria Miller called for a 20-week limit.
The home secretary said she would also "probably" back a change to 20 weeks but reiterated Number 10's view that there were no plans to change the law.
The remarks have prompted criticism from some pro-choice campaign groups.
A Downing Street spokesman insisted Mr Hunt - who was speaking ahead of the Conservative conference - was expressing purely personal views.
Later Prime Minister David Cameron stressed abortion was an "issue of conscience" and Mr Hunt was "absolutely entitled to hold an individual view".
"But people need to know the government has got no plans to bring forward any legislation in this area and any vote that does happen will be a free vote," he said.
Mr Cameron added he "personally" favoured a "modest reduction" from the current limit of 24 weeks, "because I think there are some medical arguments for that".
"But I don't agree with the 12-week limit and that's not the government's policy," he said.
'Scope for reduction'
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.
There were nearly 190,000 abortions for women in England and Wales last year.
The figures, from the Department of Health, also suggest the vast majority - 91% - were carried out in under 13 weeks.
Welsh Health Minister, Lesley Griffiths, said: "I've read Jeremy Hunt's remarks about reducing the time limit and this is something that I cannot countenance as being in the best interests of women in Wales.
"Should the UK government make any formal proposals to change the law, I will be strongly opposing such a move."
Mr Hunt told the Times he felt 12 weeks was "the right point".
He said he wants to see a significant reduction in the limit which would prevent almost all abortions past that time.
The new health secretary, who is only a few weeks into his job, said he had reached the conclusion after studying the evidence.
"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."
Labour shadow public health minister, Diane Abbott, said ministers should not be "playing politics with people's lives".
She said there was a "sustained ideological attack on the science and the rights that British women and families have fought for".
But speaking on BBC Radio 4's Today programme, Home Secretary Theresa May said the government was "right" to take the position it had, reiterating there were "no plans to reduce the abortion limit".
She added: "I think there is some scope for some reduction. My own view is probably a reduction to 20 weeks, but as I say that is a personal view of mine."
The Department of Health also said Mr Hunt had expressed his own opinion and the government's policy on abortion was clear.
'Lack of understanding'
Earlier this week, Ms Miller told the Daily Telegraph the legal abortion limit should be lowered to 20 weeks because care for extremely premature babies had improved.
Conservative MP Mark Pritchard, vice chairman of a parliamentary pro-life group, also said the limit should be cut.
"The existing laws on abortion lag well behind recent breakthroughs in science," he said.
Darinka Aleksic, from 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 hasn't looked at the scientific evidence around this at all because there's no medical basis for reducing the abortion time limit," she said.
Professor Wendy Savage, a gynaecologist who has campaigned for years on women's rights, also told the BBC she had been left "speechless" by Mr Hunt's comments.
"It does not bode well that he's the secretary of state for health. What we really should be doing is decriminalising abortion."
Elsewhere, the British Pregnancy Advisory Service's Clare Murphy said the remarks reflected "a lack of understanding of why women need later services".