A special summit of European Union leaders has been scheduled for April 10 to assess the latest twists in the Brexit saga.
Prior to their formal sit-down the leaders will take part in round-table discussions with people from Northern Ireland and the border area about their views on the UK's withdrawal from the EU.
Mr Coveney made the comments as efforts intensify to find a way through the Brexit impasse with the April 12 deadline looming. But he indicated Britain has limited options, with the only "orderly manner" being a scenario where the British parliament accepts the deal Prime Minister Theresa May's negotiators agreed to after two years of talks with the EU.
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Main image: Leo Varadkar and Emmanuel Macron in Paris today.
Barely a third of the public in Great Britain hope Northern Ireland would vote to remain in the United Kingdom, while one in six people said they would prefer it left and joined the Republic of Ireland following any future referendum on removing the Irish border.
"These are people for whom the border is a very real issue - people from communities along the border, from business, and with direct personal experience of conflict before the Good Friday Agreement", the government said in a statement, referring to the 1998 peace deal that ended three decades of violence.
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But he said he did not know "if Mr Corbyn will rise to the occasion, whether he will show leadership and be able to come up with a compromise plan with Prime Minister May".
The French President Emmanuel Macron has insisted that the European Union would not abandon Ireland, no matter what happens with Brexit. "It is far from flawless, it is not close to being a good a deal as remaining in the European Union, but it does give us all certainty for the future".
"If the United Kingdom is not capable, nearly three years after the referendum, of coming forward with a solution that is supported by a majority, it will have effectively chosen a no-deal exit on its own", he said.
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Ireland has for months refused to countenance any no-deal contingency plans for the border but recently began discussions with the European Commission over how it might be managed if its nearest neighbour crashes out of the bloc.