Walthamstow MP Creasy welcomed the announcement, but said she would not end her campaign until women in Northern Ireland could access services close to their own homes.
Currently, the Abortion Act 1967 does not apply in Northern Ireland, where abortion remains illegal except to preserve the life of the mother.
The healthcare charities and women's rights organisations represented by law firm Leigh Day who are intervening in the case are: The Family Planning Association (FPA), the British Pregnancy Advisory Service (BPAS), Birthrights, the Abortion Support Network, Royal College of Midwives, Alliance for Choice, and Antenatal Results and Choices (ARC).
An attempt to change the law in Northern Ireland to allow abortions in cases of rape, incest or serious malformation of the foetus started in the UK Supreme Court on Tuesday with harrowing accounts of women's experiences.
But that decision was overturned in June this year by three of Northern Ireland's most senior judges.
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However, Mr Azad got strong support from the Trinamul Congress, the Bahujan Samaj Party and rebel JD (U) leader Sharad Yadav. Many opposition parties said that a rally should be organised on this particular day to oppose the government's policies.
Northern Irish women who travel to England to access an abortion on the NHS will have the procedure paid for.
The Westminster-based Christian Action Research and Education (CARE) warned the government not to "overstretch its reach" after the equalities minister, Justine Greening, said a charge of around £900 to Northern Irish women having a termination in other parts of the United Kingdom was an injustice after successful campaigning on the issue by the Labour MP Stella Creasy.
724 women from Northern Ireland travelled to England for abortion care in 2016.
The Northern Ireland Assembly voted in February a year ago against legalising abortion in cases of fatal foetal abnormality and rape or incest.
In written argument before the court, Ms Lieven said both the Attorney General and the Department for Justice "are at pains to suggest there is no jurisdiction" for the Supreme Court to consider the challenge, because of the commission's "lack of standing and a failure to identify an unlawful act".
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"This case illustrates how women in even the most desperate circumstances - women who are victims of sexual assault, women who have received a tragic diagnosis of a severe foetal anomaly - are denied access to abortion care in Northern Ireland".
The appeal judges said the law in Northern Ireland should be left to the Stormont Assembly and not judges, saying that the complex moral and religious questions behind the issue should be determined by a legislature rather than a court. It's a small step that will make a significant difference to women in Northern Ireland. It has led to women being silenced, stigmatised, and criminalised.
The NIHRC's chief commissioner, Les Allamby, said in a statement: "This case has the opportunity to bring about a real change to the law on termination of pregnancy in Northern Ireland". It's time for the law to catch up with public opinion.
She believes women's lives are being put at risk.
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