Dominic Raab has refused to give Government backing to a Commons bid to make legal access to abortion a human right.
Labour MP Stella Creasy is planning to table an amendment to the forthcoming Bill of Rights to make it a fundamental right for women to get a termination.
The move comes in the wake of the US Supreme Court's decision to overturn Roe v Wade - a landmark judgement which gave woman a constitutional right to abortion.
Ms Creasy has argued that the ruling shows "we cannot be complacent about entrenching those rights in law" in the UK.
Labour MP Rosie Duffield urged Mr Raab to "send a clear signal" that Britain "respects the rights of women" following the ruling which will see millions of Americans lose their right to access terminations.
But the Justice Secretary, who is steering the legislation through Parliament, argued the amendment could lead to abortion being litigated in the courts.
Abortion is legal up to 24 weeks of pregnancy in England, Scotland and Wales under the 1967 Abortion Act, with procedures requiring sign-off from two doctors.
Repeated efforts have been made in recent years to decriminalise abortion as a separate 19th Century law contains contain criminal sanctions for both women and doctors if they do not meet the scope of the rules.
In Northern Ireland, women were given a guaranteed right to abortion under legislation backed by MPs in 2019 but terminations remain difficult to access.
Speaking during Prime Minister's Questions, Ms Duffield said: "Will he accept the cross party amendment to the forthcoming Bill of Rights which enshrines a woman's right to choose in law?"
Mr Raab replied: "The position, as she knows, is settled in UK law in relation to abortion. It is decided by [MPs] across this House, it is an issue of conscience.
"I don't think there is a strong case for change. What I wouldn't want to do is find ourselves, with the greatest respect, in the US position where this is being litigated through the courts rather than settled as it is now settled by [MPs]."
Following the clash, Ms Creasy tweeted: "Why is the bill of rights good enough to protect your freedom of speech but not your womb from being interfered with?"
Boris Johnson waded into the row over Roe v Wade last week, which he described as a "big step backwards".
Asked about the decision at the Commonwealth Heads of Government Meeting (CHOGM) in Rwanda, Mr Johnson said: "I have always believed in a woman's right to choose and I stick to that view, that's why the UK has the laws that it does."
Referring to changes to the law in Northern Ireland, he added: "We recently took steps to ensure that those laws were enforced throughout the whole of the UK."
Abortion is treated as a matter of conscience in Parliament, which means MPs are not ordered to vote for or against it by party whips.
