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 MP, who has represented Chichester in Sussex since 1997, said at the age of 60 it was time to do other things but he was committed to public service.
Mr Tyrie, who worked for BP before entering politics, has led the Treasury committee since 2010.
Veteran Tory MP Sir Alan Haselhurst is also quitting after 40 years.
Sir Alan, who has held the Essex seat of Saffron Walden since 1977, initially intended to contest the seat again on 8 June.
But, in a statement on Tuesday, the 79-year old said he had changed his mind after consulting with his family and close friends.
"When I heard the prime minister's announcement of an early general election I reacted enthusiastically with my only thought being to play my part in strengthening the position of the Conservative Party in Parliament," he said.
"I feel now that my initial instinctive response was premature...
"Whilst I have no doubt as to my capacity and commitment to carry out my representative duties I have begun to recognize that it might test the friendship and goodwill of so many people whose support I have enjoyed if I sought to do so for a further five years."
Sir Alan, who was first elected to Parliament in 1970 for Middleton and Prestwich and was deputy Commons speaker between 1997 and 2010, has faced opposition to his candidacy from within his local party.
In his resignation letter, Mr Tyrie - who opposed Brexit - said he was proud of his contribution to strengthening the select committee system and making Parliament more relevant.
Known for his forensic, and at times, acerbic style, Mr Tyrie clashed with then Prime Minister David Cameron on several occasions in his capacity as chairman of the liaison committee of senior backbenchers.
He also served as chairman of the all-party parliamentary group on extraordinary rendition, in addition to his Treasury committee duties.
"I remain deeply committed to public service," he said. "I am determined, and hopefully young enough, to contribute in other ways in the years ahead."
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.
[NEXT_CONCEPT]
Conservative MP Andrew Tyrie, who chairs the powerful Treasury Select Committee, is to stand down from Parliament at the general election.