British members of parliament are to stage a fresh attempt to make it easier for women in the North to have an abortion.
The cross-party group of MPs will attempt to force a vote in the House of Commons by tabling an amendment to the Human Fertilisation and Embryology Bill in the autumn.
The amendment to the Bill, which is passing through parliament, would allow women to have an abortion on the NHS in the North, a right they do not have now.
Labour's Diane Abbott said a woman can have an abortion in the North only if it can be shown there was evidence of a threat to her life. This was "very strictly defined", she said.
It means that every year more than 1,000 women have to pay to have the procedure carried out privately in mainland Britain, usually England.
She believed there was a "very good chance" of it being passed by MPs.
However, the proposal would face stiff opposition from the North's MPs, the majority of whom are against such a change.
There have previously been suggestions that MPs from the Democratic Unionist Party were assured the abortion laws would not be changed.
This was in return for them supporting the British government over the extension of detention without charge for terror suspects to 42 days.
The charge has always been strongly denied by the UK government, which insists no deals were made.
Ms Abbott, MP for Hackney North and Stoke Newington, told BBC Radio 4's 'Today' programme: "When it comes to abortion rights, Northern Ireland women are effectively second-class citizens.
"They don't have the same rights as women in England and Wales and Scotland. They even have fewer rights than women in the Republic of Ireland.
"The main way if you want to have an abortion, you have to travel to the UK and get one privately."
Asked if MPs should vote to change the law when the majority of the North's MPs were against it, she said: "This is a matter decided by the British parliament.
"I think it is not unreasonable that the British parliament should say that all citizens in the British Isles should have the same rights.
"The effect of the amendment would be to give women in Northern Ireland exactly the same rights to abortion with NHS funding that women elsewhere in Britain have.
"We think we have got a very good chance of getting the amendment through.
"There is a very clear majority in parliament for a woman's right to choose and we believe there is a majority to extend that to Northern Ireland."