During a visit to County Down in June, Theresa May said a Leave vote would end an open north-south border.
She also said it was inconceivable to suggest a Leave vote would not have a negative impact on the border.
However, she said she wants to see no return to old style border controls.
In her first interview as prime minister with a journalist from Northern Ireland, she said she wants to see free movement.
As home secretary, Mrs May visited County Down in June and told the BBC: "If we are out of the European Union with tariffs on exporting goods into the EU, there would have to be something to recognise that between Northern Ireland and the Republic of Ireland.
"And if you pulled out of the EU and came out of free movement, then how could you have a situation where there was an open border with a country that was in the EU and had access to free movement?"
But speaking to BBC News NI at Downing Street on Friday, Mrs May said she agreed with the Irish government and Northern Ireland Executive about not seeing a "return to the borders of the past".
She would work "closely together" with them to ensure free movement across the border, she added.
Mrs May denied that she had changed her view.
"What I said was that of course if we leave and there is a land border with a country within the European Union, that does bring a change to that relationship across the border," she said.
"All parties are clear about the intent and will to ensure we have an arrangement that isn't a return to the borders of the past."
Questioned on how the border would be policed or controlled after Brexit, Mrs May said: "We are discussing with the Irish government at the moment how we can develop these ideas in ways that are going to ensure that we deliver on the intention of all parties."
One of Ms May's first acts as prime minister was to visit Belfast, and she has pledged that the Northern Ireland Executive would be fully involved in Brexit discussions.
"We are going to make a success of Brexit, there are real opportunities for the United Kingdom," she said.
"We need to grasp those opportunities around the world but the devolved administrations will all be - and the government in Belfast will be - involved and fully engaged in the discussions we are having."
It is 100 days days since the EU referendum and the result has transformed the political landscape.
The issue of Brexit is likely to dominate the Conservative Party conference which begins this weekend.
The annual gathering in Birmingham marks Theresa May's first as leader and she will make her keynote address next Wednesday.
Although the UK voted to leave the European Union, 56% of people in Northern Ireland voted to remain.

The child was struck by the vehicle in Montrose Avenue at the junction with Burnt Oak Broadway, Edgware, at about 19:15 BST.
Police and the ambulance service attended the scene, but he was pronounced dead in hospital.
The driver of the car stopped and police said he was helping with their investigation. No arrests have been made.
The boy's next of kin have been informed.

31 October 2015 Last updated at 19:12 GMT
A group of dogs got into the spirit of the celebration at Stormont Estate on Saturday afternoon.
Claire Graham reported for BBC Newsline.
The prime minister appears to have rowed back on her comments during the EU referendum campaign that there could be Irish border controls if the UK left the EU.
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