A judge made the ruling last month.
A case had been taken by the Northern Ireland Human Rights Commission against the Department of Justice.
The judge said there should be exemptions in the law for women who were the victims of sexual crime and in cases of fatal foetal abnormality.
He said the current legal provisions in Northern Ireland breached the European Convention on Human Rights.
Unlike other parts of the UK, the 1967 Abortion Act does not apply to Northern Ireland, where abortions are illegal except where the life or mental health of the mother is in danger.
Anyone who unlawfully carries out an abortion could be jailed for life.
The judge's ruling did not change the law but had placed an onus on the Northern Ireland Assembly to legislate on the issue.
John Larkin QC, the attorney general, said at the time he was "profoundly disappointed" by the decision and was considering the grounds for appeal.
Amnesty International, the human rights organisation, said it would resist any attempt to overturn the judge's ruling.
Its Northern Ireland director, Patrick Corrigan, said: "The assembly must bring Northern Ireland's abortion laws into the 21st Century and into line with international law as a matter of urgency."
The attorney general has lodged an appeal to a High Court ruling that found Northern Ireland's abortion legislation to be "incompatible" with human rights law.