Mr Flanagan insisted Britain’s exit from the Brusses bloc would be costly for the UK and “potentially” Ireland as its closest neighbour.
But speaking on Newsnight on the BBC, the foreign minister added he did not believe the bloc would “punish” the UK for its decision to leave.
He said: “I don’t see any intent or I don’t see any disposition on the part of my EU colleagues to retribution, to punish Britain.
"I believe it’s important that the process now proceeds in an orderly manner at the earliest opportunity.
Charlie Flanagan said Brexit would be "painful" for the UK In pictures: Theresa May meets with EU's Tusk Thu, April 6, 2017
The two leaders held talks on Brexit negotiations
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European Council President Donald Tusk gestures to members of the media as he leaves 10 Downing street after talks with British Prime Minister Theresa May in central London
I don’t see any intent or I don’t see any disposition on the part of my EU colleagues to retribution, to punish Britain
“Yes, there are going to be circumstances here in Ireland. The relationship between Ireland and Britain is the warmest ever.
“I believe it (Brexit) is going to be painful for Britain, I believe it’s going to be painful for, potentially, Ireland but this isn’t our policy.
“Ireland is not withdrawing from the European Union. Ireland will remain firmly a member of the European Union.”
Mr Flanagan’s comments show a different tact to those he made last month on a visit to the Belgian capital.
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He told the EU’s Brexit negotiators his government would row behind Brussels' interests.
He confirmed that Dublin was “firmly on the side” of the remaining 27 member states as they attempt to ensure that the UK leaves the bloc on worse trading terms than it currently enjoys.
Mr Flanagan also issued an open invitation to Northern Irish voters, who backed Remain, to apply for Irish citizenship as a way of retaining their EU rights.