New Health Secretary Jeremy Hunt has said he supports a reduction in the time limit for women to have abortions from 24 to 12 weeks.
Speaking to The Times, he said he had reached his view based on evidence, not his religious belief.
He said: "I'm not someone who thinks that abortion should be made illegal.
"Everyone looks at the evidence and comes to a view about when that moment is, and my own view is that 12 weeks is the right point for it."
Mr Hunt supported lowering the abortion limit to 12 weeks in a free vote in Parliament in 2008.
"I don't think the reason I have that view is for religious reasons ... there are some issues that cut across health and morality, a bit like capital punishment does for crime," he said.
"There are all sorts of arguments in favour and against in terms of deterrence and justice, but also there is a fundamental moral issue that sits behind it. I think abortion is one of those issues."
Prime Minister David Cameron said Mr Hunt was entitled to his opinion but confirmed the Government had no plans to change the time limit for terminations from 24 weeks.
This was echoed by Home Secretary Theresa May, who told Sky News: "Jeremy has made clear that this is his personal view. The Government has no plans to reduce the limit and has got no plans to change the law on this.
"Every Cabinet minister has personal views on these issues. An issue like this is normally regarded as a matter of conscience when it comes to votes in the House of Commons, so I think it is right that somebody should be clear and open about what their personal view is," she added.
Mr Hunt is the second cabinet minister in a week to argue for lowering the abortion limit.
Women's minister Maria Miller told The Daily Telegraph she would like to see the limit lowered from 24 weeks to 20 weeks.
She said it was "common sense" to lower the legal limit at which a pregnancy can be terminated in order to "reflect the way science has moved on".
Any move to reduce the legal limit for abortion would prove highly controversial and Labour have attacked Mr Hunt.
Diane Abbott, Labour's shadow public health minister, said: "I think women and families across the country will find it staggering that the priority for this Government is playing politics with people's lives like this.
"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."
Although 91% of abortions take place before 12 weeks, opponents say that a 12-week limit would effectively prevent testing for conditions such as Down's syndrome.