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."