Donald Tusk said he had given Theresa May a deadline of Monday to make a “final offer” on the future Irish border before EU leaders decide if there is “sufficient progress” to open a second phase of Brexit talks.
The Republic of Ireland has demanded a written guarantee there will be no hard border with Northern Ireland when the UK leaves the EU.
Speaking after meeting Irish Prime Minister Leo Varadkar in Dublin, Mr Tusk said: “Let me say very clearly: If the UK offer is unacceptable for Ireland, it will also be unacceptable for the EU.
“The key to the UK’s future lies in some ways in Dublin, at least as long as Brexit negotiations continue.”
He added: “The UK started Brexit, and now it is their responsibility to propose a credible commitment to do what is necessary to avoid a hard border.”
Mrs May is due to travel to Brussels on Monday for talks with European Commission President Jean-Claude Juncker.
The Prime Minister is hoping EU leaders will give the go-ahead for the next round of Brexit negotiations, including talks on a free trade deal, at the European Council summit on December 14-15.
But the leaders of the remaining 27 EU states, including Irish premier Mr Varadkar, have a veto on triggering the second phase of talks, meaning Mrs May must be sure of support from Dublin for progress to be made.
Mr Varadkar said:”I want to make progress but I also need to make clear: the EU 27 cannot declare sufficient progress without firm and acceptable commitments on the border and that is a position shared across the political spectrum in Ireland.
“I am also prepared to stand firm if the offer falls short.”
The invisible border between the two countries following the 1998 Good Friday Agreement was enabled through the UK and Ireland’s joint membership of the EU and its single market.
In a report on Friday, MPs warned they “do not currently see how it will be possible” to avoid a customs border on the island of Ireland, if the Government pushes ahead with its aim to leave the single market and customs union.