LONDON (AP) -- British Prime Minister Theresa May met Northern Ireland's leaders in Belfast Monday in a bid to allay Northern Irish concerns about Britain's vote to leave the European Union.

May was holding talks with First Minister Arlene Foster and Deputy First Minister Martin McGuinness. The leaders of Northern Ireland's power-sharing administration were divided on the EU. Foster's pro-British Democratic Unionist Party backed the "leave'' side in the June 23 referendum, while McGuinness' Irish nationalist Sinn Fein wanted to stay in the EU.

Northern Ireland is the only part of the United Kingdom to share a land border with another EU member, the Republic of Ireland. Residents and businesses on both sides of the frontier fear a return to customs and immigration controls along the unmarked border.

May said Monday that "I have been clear that we will make a success of the U.K.'s departure from the European Union. That means it must work for Northern Ireland, too, including in relation to the border with the Republic.''

May has also visited Scotland and Wales since taking office on July 13 in a bid to ease strains the referendum result has put on the United Kingdom. A majority of voters in England and Wales backed leaving the 28-nation EU, but well over half of people in Scotland and Northern Ireland voted to remain.

The result has boosted the movement for Scottish independence, with First Minister Nicola Sturgeon saying she will do whatever it takes to keep Scotland in the EU.

The referendum result also raises questions about the future of Northern Ireland, which saw decades of violence between Irish nationalists and British unionists before a late-1990s peace settlement.

McGuinness, whose party seeks a united Ireland, has said the result should lead to a referendum on whether to join the republic.

May has said she will not begin formal negotiations to leave the EU until there is a U.K.-wide plan for British exit, known as Brexit.

"I want to assure the people of Northern Ireland that I will lead a government which works for everyone across all parts of the United Kingdom, and that Northern Ireland is a special and valued part of that union,'' she said Monday.