Health Secretary Patricia Hewitt has said she is not in favour of introducing tougher UK abortion laws.
Patricia Hewitt said she did not want to see a change in the law
She said she was against reducing the 24-week limit, but wanted to try to cut the number of late terminations.
Her comments came after a survey in the Observer suggested that 47% of UK women wanted tougher abortion laws.
Anti-abortion campaigners welcomed the results of the survey of 1,790 adults, but pro-choice groups say women need access to late abortions.
Almost half of the women surveyed wanted the legal time limit for an abortion cut from 24 weeks, the Observer said.
Another 10% of women did not agree with abortion "under any circumstances" and only 2% wanted the limit to be extended, the study suggested.
It indicated that 35% of men and 31% of women thought the current time limit for having an abortion was "about right".
Only 2% of women and 5% of men thought the last possible date after which a woman can terminate a pregnancy should be increased from 24 weeks.
ABORTION TIME LIMITS
France: 12 weeks
Germany: 12 weeks
Italy: 13 weeks
Sweden: 18 weeks
US: limits after 26 weeks
Australia: No limit
Cardinal Cormac Murphy O'Connor, head of the Catholic church in England and Wales, called for a rethink on the law.
His spokesman, Austen Ivereigh, said: "There has been a moral awakening over the last few years about abortion; the British public have been undergoing a reality check."
But Ms Hewitt said she would not want to see any change in the law, although she said it was right to try to cut the number of late terminations.
She told Sky News: "I would not myself want to see the legal maximum changed and this quite rightly has always been left to backbench members of Parliament in private members' bills and not government bills.
"We really want to keep reducing the number of late abortions."
She said the important thing was to make sure that a woman who requested an abortion in a very late stage of pregnancy "gets very good counselling and advice before she makes that decision".
Ms Hewitt said "nobody wants to see a late abortion" and "nobody wants to have a late abortion".
"Fortunately there are very few of them and if we can get that level down even further so much the better," she added.
Of all the abortions carried out in England and Wales, government figures show that fewer than 2% occur after 20 weeks.
The majority - just under 90% - are carried out in the first 12 weeks of pregnancy.
Julia Millington, of the Pro-Life Alliance, told the Observer the survey's findings were "very encouraging".
But Toni Belfield of the Family Planning Association, which opposes any reduction, said there needed to be access to late abortion after 20 weeks.
This was because "a woman may not find out she is pregnant until 18 or 19 weeks, or be in a non-consensual relationship, or be told about a foetal abnormality".