The Prime Minister and his Irish counterpart said talks were "detailed and constructive" as discussions continue in Brussels today.
The Irish Taoiseach will meet the PM for talks today but has warned of the difficulty of achieving a Brexit deal by the Brussels summit.
An agreement has been reached to establish a new round of talks between the main parties in Northern Ireland, it has been announced.
Leo Varadkar has praised the Prime Minister for "honouring" her promise to avoid a hard border in Ireland with the draft withdrawal agreement.
Downing Street has released a statement saying the Prime Minister and Irish Premier had agreed the backstop should “only be a temporary arrangement”, but Leo Varadkar said he would not accept a Brexit deal which gives the UK unilateral power to halt the backstop.
The Taoiseach of Ireland Leo Varadkar has said the lack of agreement over a workable Irish Border solution for Brexit is 'fraying relationships' between the UK and Ireland
So-called "overflight rights" are guaranteed by international treaties rather than EU membership, a Number 10 spokeswoman said
The pair are to discuss Brexit negotiations the European Commission's draftwithdrawal agreement and suggested guidelines
Theresa May is hoping to offer a new deal which satisfies the DUP and Ireland
Kate Hoey, the Labour MP for Vauxhall spoke to Julia Hartley-Brewer after a deal on the border to the Republic fell apart at the eleventh hour
The DUP's decision came after an announcement had already been made about a deal over the border
The Exiting the EU Committee in the House of Commons said this appeared possible if the UK leaves the single market and customs union
The Prime Minister is in Sweden for a major EU summit in Gothenburg
Leaders from the EU member-states are scheduled to meet later on Thursday
Bernard Purcell, editor of Irish World, spoke to Julia Hartley-Brewer about the reported call by the Irish government for a border on the Irish Sea