BELFAST - British Prime Minister Theresa May and Irish leader Leo Varadkar began talks with political parties in Northern Ireland on Monday to urge them to restore devolved government and avoid the introduction of direct rule from London.

The British province has been without a devolved executive for over a year since Irish nationalists Sinn Fein withdrew from a power-sharing government with their arch-rivals, the Democratic Unionist Party (DUP).

The two sides said on Friday progress had been made and a breakthrough was possible this week.

May and Varadkar met near Northern Ireland's Stormont parliament on Monday, ahead of their individual meetings with the parties, Britain's Northern Ireland Office said.

A failure to form a government would probably result in the introduction of direct rule from London for the first time in a decade and reignite a diplomatic dispute over what role the Irish government should have in the region.

It could also further destabilise the delicate balance between Irish nationalists and unionists who, until last year, had run the province since 2007 under the terms of the 1998 Good Friday peace accord which ended three decades of violence.

The meetings come as Britain bids to secure a breakthrough in talks with the European Union on the terms of its exit from the bloc, which could have dramatic implications for Northern Ireland.

The future trading relationship will help determine whether physical infrastructure will be required to control the border between the region and the Republic of Ireland, which will become an EU frontier.

EU negotiator Michel Barnier last week warned that if Britain proceeded with plans to leave the EU's single market and customs union, border checks would be unavoidable.

Varadkar on Sunday called for "clarity and urgency" from London in laying out exactly what kind of a post-Brexit deal it wants.

May, who is hoping to seal a transition deal with the EU next month to smooth Britain's exit, on Sunday said she would set out what it wants from Brexit in a series of speeches over the next few weeks.

The DUP and Sinn Fein have failed to reach agreement on a number of contentious issues, including the introduction of same-sex marriage, which is illegal in Northern Ireland but legal in the rest of Britain and Ireland.

Rights for Irish-language speakers and funding for inquests into deaths during the decades of Protestant-Catholic sectarian violence before 1998 have also proved contentious.

Reuters