The government has refused a call to guarantee the right to abortions in its forthcoming new "British bill of rights".
Justice Secretary Dominic Raab, who is steering the proposed charter through parliament, on Wednesday told MPs he did not see a case for the protection.
The issue of access to abortion care has jumped up the agenda following the US Supreme Court's decision to overturn legal protections across the Atlantic.
Millions of women in the US are losing their right to abortions, with over half of US states expected to restrict or ban the medical procedure.
Speaking at prime minister's questions Labour MP Rosie Duffield asked the government to "send a clear signal" that "Britain respects the rights of women".
"Will he accept the cross-party amendment to his forthcoming Bill of Rights, which enshrines a woman's right to choose in law?" she said.
The cross-party amendment, expected to the tabled by Labour MP Stella Creasy, would enshrine the right to the medical procedure in British law.
But Mr Raab, who was deputising for Boris Johnson at the session, said: "The position as she knows is settled in UK law in relation to abortion.
"It's decided by members across this house. It's 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 a greatest respect to the US position where this is being litigated through the courts rather than settled, as it is now settled, by honourable members of this house."
Mr Raab abstained in a vote on decriminalising abortion in March 2017, and again in 2020 abstained on the introduction of buffer zones around abortion clinics to prevent protesters from harassing patients.
Abortions are still by default deemed a criminal act in England, Scotland and Wales under the 1967 Abortion Act.
Pregnancies may only be terminated under the terms of the act with the confirmation of two doctors, who must agree that continuing with the pregnancy would be riskier for the physical or mental health or the woman than aborting it.
Terminations can legally be carried out within the first 24 weeks of pregnancy in England, Scotland and Wales.
But they can only be performed after the 24 week cut off point in a highly limited number of contexts - such as when the mother’s life is at risk or the child will have a severe disability.
For years, abortion providers, charities, medical bodies, and MPs have been calling for abortion to be decriminalised in the UK. They want to see abortion law extricated from criminal law and monitored in a same way to other medical practices - with the British Medical Association in favour of the decriminalisation of abortion in the UK.
The right to abortion is mentioned in some national constitutions. The Irish constitution in 2018 was amended by referendum to state that “provision may be made by law for the regulation of termination of pregnancy”. This replaced an earlier amendment banning abortions.
In France over the weekend politicians representing the governing majority expressed support for amending that country’s law to include abortion protections.
Prime minister Elisabeth Borne said the government would support the constitution amendment bill “wholeheartedly”, adding: “For all women, for human rights, we must set this gain in stone. Parliament must be able to unite overwhelmingly over this text.”
