Video report by ITV News political correspondent Paul Brand
Theresa May has said her commitment to avoiding a hard border between Northern Ireland and the UK is "unshakeable."
Her speech comes 48 hours ahead of her meeting in Brussels, where she aims to reopen Brexit talks with the European Commission president Jean-Claude Juncker.
Speaking in Belfast she said: "I'm here today to affirm my commitment, and that of the UK Government, to all of the people of Northern Ireland, of every background and tradition."
She added that she was committed to the Good Friday Agreement and its successors.
She said she wanted to "affirm my commitment to delivering a Brexit that ensures no return to a hard border between Northern Ireland and Ireland, which is unshakeable".
In her speech Mrs May suggested a time limit to the backstop might be a potential solution.
Earlier today former Northern Ireland first minister Lord Trimble said he is considering a legal challenge to the backstop elements of the EU Withdrawal Agreement over concerns about its impact on the Good Friday Agreement.
He told BBC Radio 4's Today programme: "We are exploring this possibility and we are concerned at the way in which the Withdrawal Agreement that our Prime Minister agreed actually turns the Belfast Agreement on its head and does serious damage to it."
During her speech Mrs May acknowledged that her deal needed to be changed in order to win a majority in Parliament.
She said that while she had tried to make the case for the Withdrawal Agreement, she had to accept it would not get through Parliament in its current form.
"I fought hard to make the case for the deal as it stands," she said.
"I believed it could command a majority in the House of Commons but I have had to face up to the fact that in its current form it cannot and the need for changes to the backstop is the key issue.
"While there were those in Northern Ireland who favoured it, it is also true that the backstop is not supported by the two main Unionist parties here and it also influenced MPs in England, Scotland and Wales in voting against the deal."
Acknowledging the "real anxieties" felt in Northern Ireland she said: "I understand what a hard border would mean."
She said: "There will be no new regulatory borders between Northern Ireland and the rest of the UK, and added "there will be protection for all existing cross-border cooperation."
On Thursday Mrs May is expected to push the European Commission to reopen talks around the Withdrawal Agreement, making a bid for alternative options to the backstop.
It will be the prime minister's first official meeting in Brussels since MPs overwhelming voted against her deal because of the backstop.
Meanwhile in Westminster, the working group bringing together senior Eurosceptic and former Remain-supporting Tories will continue efforts to agree alternatives to the backstop along the lines of the Malthouse Compromise.
Talks involving Conservatives including Brexiteers Iain Duncan Smith, Theresa Villiers, Steve Baker and Owen Paterson along with former Remainers Nicky Morgan and Damian Green will continue in Whitehall, chaired by Brexit Secretary Stephen Barclay.
The first meeting on Monday was described as “detailed and constructive” by the Brexit department.
But Brussels has restated its opposition to any attempt to reopen the Withdrawal Agreement, insisting the backstop was the “only operational solution” to the border question.
Watch in Theresa May's full speech: