Karen Bradley says Northern Ireland abortion law should not be imposed
Westminster should not "impose its will" on Northern Ireland by changing abortion laws, the government says.
Northern Ireland Secretary Karen Bradley said she would personally like the law to be changed.
But she said the matter was devolved and "should be decided by the people of Northern Ireland".
She was responding to cross-party calls for a change in the law that criminalises abortion in Northern Ireland.
In the House of Commons, both sides set out their case in an often emotional debate, with Democratic Unionist MPs saying it should be left to politicians in Northern Ireland.
But Conservative MP Heidi Allen said a "window of change" had presented itself as she recalled her own "incredibly hard decision" to have a termination.
"I have been there," she said.
"I am making it my business."
Labour MP Jess Phillips also shared her own experience of abortion and read out accounts she had received from Northern Irish women who had travelled to England, Scotland and Wales for the procedure.
But the DUP's Sammy Wilson said the debate had "two sides" and that he was "not embarrassed" about the law in Northern Ireland, saying there were people living there today who would otherwise have been "discarded and put in a bin before they were ever born".
His remark drew criticism from other MPs, and the SNP's Hannah Bardell later said this was a "a disgusting way to describe the choices that women have to make".
Conservative MP Anna Soubry said the law as it stood in Northern Ireland was "cruel" and "repressive". But her fellow Tory MP Maria Caulfield accused campaigners of telling women in Northern Ireland "that the women in Westminster know best", saying their campaign "flies in the face of women's rights and women's choices".
After the debate, Equalities Minister Penny Mordaunt said MPs had sent a message to Northern Ireland's politicians that if they did not act, "we will".
Following last month's Irish referendum result, Northern Ireland will soon be the only part of either the UK or Ireland where abortion is illegal unless there is a serious risk to a woman's life or health.
Labour MP Stella Creasy is leading calls for parts of the 1861 Offences Against the Person Act - the legislation that still governs abortion in Northern Ireland - to be repealed.
In 1967, the 1861 act was amended so abortions were legal in England and Wales - but this was not extended to Northern Ireland.
Ms Bradley said there were clearly a range of views on the issue.
But abortion had "long been devolved" she said, and "it would not be appropriate for Westminster to seek to impose its will" on Northern Ireland.
"Personally I want to see reform in Northern Ireland - but it is a matter for the people of Northern Ireland," she said, adding that if the matter came before the House of Commons it would be a "free vote" with MPs able to vote with their conscience.
Ms Bradley said Ireland's referendum was "specific to Ireland" and there were "significant differences" with the situation in Northern Ireland.
But setting out her case, Ms Creasy - who was backed by MPs from other parties - said the "impact" of last month's referendum had been the trigger for the debate.
Tory rock and DUP hard place
By Gareth Gordon, BBC News NI political correspondent
On one hand, Theresa May's motivation for resisting calls to intervene to change Northern Ireland's abortion laws is obvious - for one thing she does not want to upset the Democratic Unionist Party apple cart.
On the other, where will this apparent Conservative revolt (if that's what it is) end - and how big must it grow before she cannot resist it any longer?
And then there is the DUP itself. It possesses the "nuclear button" of threatening to bring down the government.
But press it and we could be looking at (in DUP terms) a post-apocalypse world in which the Labour Party is in power and Jeremy Corbyn is prime minister.
The Walthamstow MP said: "150 years is a long time to wait for social justice," adding: "Men and women will never truly be free whilst one cannot control what happens to their own body."
She said she had received abuse online for her campaign, calling her a "disgrace to humanity".
"Frankly, women get the blame whatever we do in these situations."
Ms Creasy called for the government to offer a date for a vote to test the will of the Commons on the subject.
The DUP's Ian Paisley said her proposal would create a "massive hole" in the law in Northern Ireland and not allow doctors the right to conscientious objections against abortion.
And another DUP MP, Sir Jeffrey Donaldson, said law and policy should "affirm and uphold" the rights of both mothers and unborn children, paying tribute to Sinn Fein politicians who shared his anti-abortion stance and saying it was "nonsense" to say his party was alone in its view.
"It is for the people of Northern Ireland through the Northern Ireland Assembly to decide what the law on abortion should be," he added.
Sinn Fein vice president Michelle O'Neill welcomed the Westminster debate, describing it as a "first step" on the road to abortion reform in Northern Ireland.