Among the topics May discussed with Enda Kenny were the open border between Britain and Ireland and the importance of upholding the Irish peace process, Efe news reported.
"I firmly believe that we can make a success of Brexit and take our relationship forwards not backwards," said May, referring to the "deep and important" relationship between Britain and Ireland.
The border between the two countries has been open since the Common Travel Act was passed in 1923, allowing free travel between Ireland, Britain, the Isle of Man and the Channel Islands.
However, following Britain's decision on June 23 to leave the European Union, the open border between Ireland and Britain may have to be shut.
May spoke of keeping the open borders, insisting that "nobody wants to return to the borders of the past" and that the two countries should also collaborate to strengthen their exterior frontiers.
The two heads of state agreed that maintaining the peace process in Northern Ireland was a priority.
During the Brexit referendum, 56 per cent of Northern Ireland voted to remain in the EU.
This resulted in discussions about Northern Ireland remaining in Britain or joining Ireland, with even ex-IRA member and Deputy First Minister of Ireland Martin McGuinness calling for a referendum for the reunification of the island.
"We reiterated the importance of the partnership between our two Governments in supporting the peace process and in contributing to stability and continued progress in Northern Ireland," Efe news quoted Kenny as saying.
The meeting between Kenny and May was the first since May's inauguration on July 13 and was followed by a joint press conference at 10 Downing Street.
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