The Irish Prime Minister has sugested Britain and the European Union (EU) could form a special customs after Brexit, adding that "time is running out" to find a workable border arrangements in Northern Ireland.
Leo Varadkar said avoiding a hard border on the island of Ireland was "the challenge of this generation".
"Every single aspect of life in Northern Ireland could be affected by Brexit," he told an invited audience at Belfast's Queen's University during his first official visit to the British province since becoming Irish leader in June.
Varadkar said politicians who favour a hard Brexit have already had 14 months to come up with a plan, which they have failed to present.
He said: "If they cannot, and I believe they cannot, we can then talk meaningfully about solutions that might work for all of us."
The Irish leader said if the UK did not want to remain in the EU's customs union, it might be possible to set up a specially-created union between the UK and EU.
"After all, we have one with Turkey," Varadkar said. "Surely we can have one with the United Kingdom."
Varadkar also suggested that if the UK does not want to remain in the single market, it could agree "a deep free trade agreement" with the EU and rejoin the European Free Trade Association, to which it belonged before it was an EU member.
The Irish Prime Minister noted that the EU would meet in October to decide whether sufficient progress had been made in the first phase of exit talks to allow the negotiations to proceed to the next phase, concerning future trade arrangements.
He stressed that Northern Ireland's voice needed to be heard ahead of that crunch decision and urged politicians there to resolve their differences and get power-sharing at Stormont back on track.
Issues surrounding Brexit fall into sharp focus on the island of Ireland. The Irish Republic and Northern Ireland are closely economically integrated, while the Irish and UK governments are also joint guarantors of the 1998 Good Friday Agreement that ended nearly 30 years of violence in Northern Ireland.
Varadkar said: "Today we need an answer to the question, of who do we – and others in Europe – talk to in Belfast? Who will speak for Northern Ireland and her 1.8 million people?
"Time is running out, and I fear there will be no extra time allowed."
Varadkar is later due to meet Democratic Unionist Party (DUP) Sinn Féin, the Social Democratic and Labour Party and the Alliance Party.
The meeting with DUP leader Arlene Foster comes days after a row between the party and the Irish leader over the Irish border after Brexit.
Varadkar had said he refused to design a border for Brexiteers, but DUP MP Sir Jeffrey Donaldson hit back that "megaphone diplomacy from Dublin" would not sort out the border issue.
"It is better to have dialogue than what we've seen in recent weeks which is the Irish government making statements about a border in the Irish Sea which is totally impractical and a non-starter," said Donaldson on the BBC's Good Morning Ulster today (4 July).
He added: "We want a comprehensive free trade and customs agreement, we want a common travel area. These are the objectives we've set, we're negotiating with Brussels, but Dublin is currently disengaged."