Dominic Raab ruled out creating a new layer of protection for abortion rights in the UK.
The Deputy Prime Minister and Secretary of Justice said he would not add a proposed amendment to the legislation he was pushing through the Commons.
Some MPs have called for a change that entrenches the right to vote after the overthrow of Roe v Wade in the US.
Labor’s Stella Creasy has said she will formally table the amendment to the UK Bill of Rights.
Mr Raab was asked by another Labor MP, Rosie Duffield, about the move when he stood up for Boris Johnson in the Prime Minister’s question.
He said: ‘The position, as she knows it, is rooted in British legislation regarding abortion.
‘It is decided by honorable members throughout this House. It’s a matter of consciousness. I do not think there is a strong argument for change.
“What I would not want to do is to find ourselves, with the utmost respect, in the American position where it is litigated by the courts rather than settled as it is now decided by honorable members of this House.”
Ms Creasy tweeted afterwards: ‘Why is the Bill of Rights good enough to protect your freedom of speech, but not your womb against interference?’
The Supreme Court’s move to scrap the entire U.S. for access to abortion is expected to result in about half of the states banning it altogether.
While abortion is legal in the UK, it is only constitutionally entrenched in Northern Ireland as the rest of the country does not have a written constitution.
Former Labor Minister Diana Johnson said she was afraid far-right US groups seeking to turn back British abortion protection would gain “renewed impetus” through the US move.
In recent days, there have been renewed calls for ‘buffer zones’ to be set up around abortion clinics to prevent protests.
During the G7 summit earlier this week, Mr. Johnson asked about the court’s decision on CNN.
He said: ‘I want to emphasize that this is not our court, this is not our jurisdiction.
‘So in a sense I’m saying it’s for the United States, it’s not for the United Kingdom.
‘But the Roe v Wade ruling, when it came out, was psychologically of great importance to people around the world, and it spoke of the promotion of women’s rights, I think.
‘And I’m sorry for what seems to me to be a step backwards. But you know, I’m talking like someone looking in from the outside. ‘
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