Tory leader Michael Howard says he would support reducing the legal time limit for abortions to 20 weeks.
There are fears a change in abortion law would hit teenagers
Current rules allowing procedures, for medical reasons, until the 24th week of pregnancy are "tantamount to abortion on demand", he told Cosmopolitan.
Tony Blair said there were no plans to change the law but "debate would continue" on the "difficult issue".
The Family Planning Association says a reduction would particularly affect young women who often seek help later.
More than 180,000 women in England and Wales had terminations last year, of which fewer than 1% were carried out between 22 and 24 weeks.
In the Cosmopolitan interview, reported in the Observer, Mr Howard said: "I believe abortion should be available to everyone, but the law should be changed.
"In the past I voted for a restriction to 22 weeks and I would be prepared to go down to 20."
All three main parties offer a free vote on abortion and Mr Howard stressed this was his personal view.
Shadow home secretary David Davis said he understood Mr Howard had been signalling that a Conservative government would allow a Commons vote on the issue.
Tony Blair and Liberal Democrat leader Charles Kennedy also gave their views during interviews, conducted as part of the magazine's "High Heeled Vote" campaign.
Mr Blair said it was a "difficult issue".
"However, much I dislike the idea of abortion, you should not criminalise a woman who, in very difficult circumstances, makes that choice.
"Obviously there is a time beyond which you can't have an abortion, and we have no plans to change that although the debate will continue."
Mr Kennedy said he had previously voted for a 22-week limit but medical advances mean "I don't know what I would do now".
Anne Weyman, chief executive of the Family Planning Association, said: "Young women make up a high percentage of late abortions: they often just don't come forward.
"They hope its not true, or might have irregular periods if they are young, so they may not be sure they are pregnant.
"There are also issues around older women who are peri-menopausal and may think there's no chance they are going to be pregnant."
She added: "What is the benefit to women, or to the potential child, of forcing a woman to have a baby?"
Anti-abortion group the Pro-Life Alliance "congratulated" Mr Howard on his new stance, but said it did not go far enough.
"We acknowledge it will be difficult to abolish abortion overnight, but the lead given by Mr Howard will inspire us in our forthcoming campaigns," said a spokesman.