Right To Life has asked supporters to urge MPs to vote against the amendment, known as NC55, which it said would make the Abortion Act 1967 redundant.
After the Act was passed, abortion was permitted up to 28 weeks until 1990, when the time limit was reduced to 24 weeks unless there is a “substantial risk” of disability.
The Society for the Protection of Unborn Children (SPUC) has also urged its members to write to their MPs.
The group explained that the amendment would allow abortion up to birth by repealing sections of the Offences Against the Person Act 1861, which prohibits the administration of drugs or the use of instruments to cause a miscarriage, and excluding abortion from the Infant Life (Preservation) Act 1929.
The move follows the failure of a similar attempt to change abortion legislation in July 2020 through an amendment to a domestic abuse bill.