The embryology bill has already prompted protests over abortion law
MPs have tabled an amendment to the Human Fertilisation and Embryology Bill to give women in Northern Ireland the same abortion rights as in Britain.
The 1967 Abortion Act was never enacted in Northern Ireland.
The amendment was tabled on the last day of the parliamentary session and MPs will not debate the amendment until the Autumn at the earliest.
All the Northern Ireland parties with MPs at Westminster oppose moves to extend abortion rights.
But there is no guarantee that the amendment tabled by Labour MP Diane Abbott will be called by the Speaker for debate.
Issue of equality
Ms Abbott says she believes there is "a very good chance" of it being passed by MPs - but it would face stiff opposition from Northern Ireland MPs who are against such a change.
There was speculation last month, at the time of the vote on detaining terror suspects for up to 42 days, that assurances were given to the Democratic Unionist Party that the abortion legislation would not be extended to Northern Ireland.
The nine DUP MPs were crucial to the government winning that vote - although Gordon Brown insisted there had been no deals.
Despite this, supporters are hopeful that the amendment may be successful as the abortion time limit that applies to the rest of the UK was discussed as part of the HFE legislation, so it would be difficult to rule it out of order.
The Northern Ireland amendment was tabled on Wednesday in the name of Ms Abbott and backed by fellow left-wing MPs John McDonnell and Katy Clark, plus Tories Jacqui Lait and John Bercow and Lib Dem Evan Harris.
Ms Abbott says it is an issue of equality.
"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 and they even have fewer rights than women in the Republic of Ireland," she said.
"So really the main way, if you want to have abortion and you're a woman in Northern Ireland, you have to travel to the UK. So every year thousands of women pay with their own money to have an abortion here.
"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."
Democratic Unionist Party MP Jeffrey Donaldson said all the main political parties in Northern Ireland and the four main churches had written to MPs opposing any change in the law.
"The reason why the law is different in Northern Ireland is because that is what the people of Northern Ireland want," he said.
"We will be vigorously opposing any move to override the wishes of the people of Northern Ireland and the Northern Ireland Assembly."
SDLP leader Mark Durkan said: "I had feared these amendments proposing such an extension would have been tabled at an earlier stage, but it comes as no surprise that it has happened now.
"The SDLP with full democratic conscience will do everything we can to oppose these plans and will do so on behalf of the people who have elected us and on behalf of those human beings who can be saved if we can effectively curb and hold back the extension of this Act."
If the amendment was debated, there would be a "free vote", which means MPs can vote with their conscience.
The remaining stages of the controversial HFE Bill were due to be debated earlier this month, but this has now been delayed until the autumn.