Prime Minister Theresa May is to hold a bilateral meeting with the Irish Taoiseach in Brussels later on Thursday.
The border between Northern Ireland and the Republic is one of the most vexing issues facing Brexit negotiators.
Irish premier Leo Varadkar is hoping to agree guidelines on the future relationship between the EU and UK at this week's European Council summit of leaders, with the focus on progress in the negotiations.
On Monday the UK and EU agreed terms for a transition period.
The draft text of a withdrawal treaty includes an agreement that there must be a backstop solution to ensure there is no hard border on the island of Ireland if no other answers are found.
The Irish Government has insisted the UK has provided a "cast-iron guarantee" that will ensure no physical infrastructure, checks or controls at the border between Northern Ireland and the Republic after withdrawal.
Without any other broader trade solution, Northern Ireland would continue to follow EU regulations which affect the island.
Most of the detail around how the border arrangements would operate have not been agreed.
Mr Varadkar said: "On Friday we will meet in Article 50 format to discuss the Brexit negotiations.
"This is an important moment in the Article 50 negotiations and it is hoped that we can agree guidelines on the future relationship between the EU and the UK.
"I am pleased that the UK has now agreed that a backstop solution to avoid a hard border proposed in December, will form part of the legal text, and that all the issues identified by the EU side in the draft will be addressed, to deliver a legally sound solution to avoid a hard border on our island.
"Prime Minister May confirmed this in a letter to (European Council) President (Donald) Tusk on Monday."
Discussions over Thursday and Friday will also focus on jobs, growth and competitiveness, external relations, the future of Europe and particularly digital taxation, and further and better economic and monetary union.
On Thursday, European leaders will discuss and adopt conclusions on jobs, growth, competitiveness including the Single Market, social issues, and trade.
They will also consider external relations including Turkey and the Western Balkans.
Leaders' discussions are intended to facilitate open exchanges of views on the future of Europe.
Mr Varadkar added: "The main focus this evening will be on digital taxation.
"We believe that global solutions are needed to ensure that tax is paid by companies where value is created and profits are generated, reflecting the highly international nature of the digital economy.
"I will strongly argue that the EU should wait for the OECD to complete its work before deciding on how to act, and should only do so in the context of agreement on an international level."