She spoke on her first visit since taking office to Northern Ireland, which has what would become the United Kingdom's only border with the EU after Brexit.
"Nobody wants a return to the borders of the past," May said in Belfast, where she met Northern Ireland's First Minister Arlene Foster and Deputy First Minister Martin McGuinness.
"What we do want is to find a way through this that is going to work and deliver a practical solution for everybody," May said in televised comments.
British PM heads to Northern Ireland for Brexit talks
Cross-border relations with the Republic of Ireland are a prime concern for Northern Ireland in negotiations on Britain's departure from the European Union, and May said Belfast would be involved in the talks.
Britain and Ireland share an open-border Common Travel Area (CTA) that dates back to the 1920s, continuing arrangements from before Irish independence.
However, questions and concerns have been raised about what Brexit would mean for the CTA and for both economies on the island of Ireland -- and whether the reimposition of border checks could undermine the peace process.
Northern Ireland was riven by three decades of sectarian violence up until the 1990s over whether it should remain part of Britain or join with the Republic to the south.
May took office on July 13 after David Cameron resigned following the June 23 referendum.
While a majority across the kingdom voted for the UK to leave the EU, a majority in Northern Ireland, -- like Scotland and London -- voted for the UK to stay.
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May has put British unity at the heart of her premiership. Since taking office, she has visited both Scotland and Wales.
On Friday, Foster and Irish Prime Minister Enda Kenny said Brexit must not mean the establishment of a "hard border" between Northern Ireland and the Republic of Ireland.
"Hard borders would not be accepted in the south or the north," said Kenny.
"We have difficulties but I expect us to retain the Common Travel Area. It's a fundamental part of who we are."
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