The UK is committed to a "close and special partnership" with the Ireland post-Brexit, the Prime Minister has told new Taoiseach Leo Varadkar.
The two leaders discussed a variety of issues during a phone call on Thursday.
During the exchanges, a Downing Street spokeswoman said Mrs May had assured Mr Varadkar of her steadfast commitment to the terms of the Good Friday Agreement.
The Government's adherence to the 1998 peace accord, in particular the requirement for it to act with "rigorous impartiality" in Northern Ireland, has been questioned by some in the wake of Mrs May's anticipated parliamentary deal with the DUP.
"The Prime Minister spoke to Leo Varadkar on the phone earlier today to offer her congratulations on becoming Taoiseach," said the Downing Street spokeswoman.
"The Taoiseach expressed his deepest sympathies for recent tragic events and said the thoughts of the Irish people were with the people of London at this time.
"Both leaders agreed on the importance of continued cooperation between the two countries and the Prime Minister said she was personally committed to a close and special partnership with Ireland as the UK embarks on leaving the European Union.
"They also spoke about a crucial need for the parties in Northern Ireland to come together to form a fully functioning Executive by the 29 June and how both leaders would continue to engage closely on this important issue.
"The Prime Minister also emphasised her steadfast commitment to the Belfast Agreement and its successors and the two leaders agreed to meet in person at the earliest possible opportunity."