Pro-life campaigners will now concentrate their efforts on repealing Ireland's new laws on abortion.
The comments from pro-life groups come after President Higgins signed the Protection of Life During Pregnancy Bill into law earlier today.
Irish law now allows for the termination of a pregnancy when a woman's life is at risk in three circumstances: in the case of a medical emergency, medical treatment for an illness such as cancer, and in cases of suicide because of the pregnancy.
The Pro Life Campaign has described the signature of the bill as "a very sad day".
President Higgins earlier signed the bill into law without referring it to the Supreme Court to test its constitutionality.
Legal Editor at the Irish Independent, Dearbhail McDonald, said the members of the Council of State - including former President Mary Robinson and former Taoiseach John Bruton - felt that such a referral was unnecessary.
"They recommended that the abortion legislation shouldn't be referred to the Supreme Court, that it should be allowed to be signed into law, and no doubt will be challenged in the courts through individual cases."
Meanwhile, Eamon Gilmore has described the signing of the bill as a key milestone in Irish law.
He said the enactment of the legislation, 21 years after the Supreme Court ruling on the X Case, is a historic moment, particularly for the women of Ireland.