The UK Prime Minister held "robust but constructive" with the European Commission President Jean-Claude Juncker in Brussels this morning as the Brexit deadlock continues.

Theresa May arrived in Brussels after her two-day visit to Northern Ireland earlier this week.

In a joint statement following this morning's meeting, the leaders said their teams will hold further talks aimed at finding out whether it is possible to find a breakthrough " that would gain the broadest possible support in the UK Parliament and respect the guidelines agreed by the European Council."

Mr Juncker again warned Mrs May that the Brexit Withdrawal Agreement - including the Irish backstop - is not open for re-negotiation.

He said the deal "represents a carefully balanced compromise between the European Union and the UK, in which both sides have made significant concessions."

He said the EU was open to expanding on the political declaration that complements the agreement, "in order to be more ambitious in terms of content and speed when it comes to the future relationship between the EU and the UK."

He warned however that the any new  wording would have to be agreed by the European Parliament and the EU27.

European commission President Jean-Claude Juncker meets with British Prime Minister Theresa May in Brussels, 07-02-2019. Image: Etienne Ansotte/European Commission/dpa

Mrs May said she had described the situation she faces in the UK Parliament and "the motivation behind last week's vote in the House of Commons seeking a legally binding change to the terms of the backstop."

She said she had " various options for dealing with these concerns in the context of the Withdrawal Agreement in line with her commitments to the Parliament."

The two leaders have agreed to meet again before the end of February.