UK and Ireland in push to break Northern Ireland deadlock

The Democratic Unionist Party (DUP), which holds the key to forming a government and is an ally of May's government in London, refused to meet with Varadkar because he is the leader of another party.

"I think we are now at the point of where it is time for the locally elected representatives to find a way to work together and to deal with and tackle the many pressing issues facing Northern Ireland," May said after the talks.

She insisted that "it has been thirteen long months since we last saw devolved government here."

The government fell in January last year over a series of issues, including a scandal surrounding a renewable heat scheme and the departure of deputy first minister Martin McGuinness, the nationalist Sinn Fein's main figure, due to ill health.

An election in March remained inconclusive and talks have been dragging on ever since.

"While some differences remain, I believe that it is possible to see the basis of an agreement here," May said after Monday's talks.

She insisted that the DUP and Sinn Fein "have been working very hard to close the remaining gaps."

Varadkar said he was "very hopeful that those two parties will be able to come to agreement this week."

DUP leader Arlene Foster noted that there was "very good progress", but that "there isn't a deal yet."

"We will keep at it and continue to work on that progress," she said.

Sinn Fein's leader, Mary Lou McDonald, said she believed that "we are close to an agreement which, certainly, we can put to our grassroots and to the community as a whole."

The deadlock in Northern Ireland has jeopardised the power-sharing between unionists and nationalists, put in place after the 1998 Good Friday peace agreement.

Hard border

It also comes as Brexit - and the prospect of a 'hard border' with the Republic of Ireland - threatens stability and cooperation brought about by the agreement across the border.

At their meeting in Belfast, May and Varadkar agreed to work together to find solutions to avoid a hard border.

The Irish prime minister insisted after the meeting that "the best option by which we can avoid any new barriers [is] through a comprehensive customs and trade agreement involving Britain and Ireland."

He said that he agreed with May "to work together at official levels to see if we can explore solutions to see how that can be achieved in the coming weeks and months."