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Taoiseach (Irish Prime Minister) Enda Kenny has said Brexit talks should take into account the possibility of a future poll on a united Ireland.

He said negotiators should consider that a clause in the Good Friday Agreement could be triggered that would result in the calling of a referendum.

He added it required "clear evidence of a majority of people wishing to leave the UK and join the Republic".

The new Northern Ireland secretary ruled out a poll earlier on Monday.

James Brokenshire, in his first visit to Northern Ireland since taking up his post last week, said there was "a clear, constitutional settlement in relation to the border poll and it's also clear to me that opinion does not support a change".

Mr Kenny made his remarks as he spoke to reporters at the annual MacGill Summer School in Glenties, County Donegal, where he delivered a speech about the implications of the UK's exit from the European Union.

He told Irish broadcaster RTÉ: "The discussions and the negotiations that take place over the next period should take into account the possibility - however far out it might be - that the clause in the Good Friday Agreement might be triggered.

"In that, if there's clear evidence of a majority of people wishing to leave the United Kingdom and join the Republic - that that should be catered for in the discussions that take place."

Speaking to the audience at the summer school, he said he had "not favoured the holding of a border poll" because the necessary conditions, set out under the Good Friday Agreement did not exist.

However, he added that the forthcoming negotiations should foresee the possibility that support for joining the Republic "in an all-island situation" could grow in Northern Ireland as a result of Brexit.

He added: "It may be, in the eyes of some, a fanciful theory but who knows what happens in 10, 20 years time?"

The taoiseach also referred to the reunification of Germany as an example of how the process could be considered.

"In the same way as it was possible for the former East Germany to be associated with West Germany, and not to have to go through a very long and tortuous process to join the European Union - and these negotiations should take these kinds of things into account as well," Mr Kenny said.

At the same event on Sunday, the Republic of Ireland's opposition leader said he hoped the UK's European Union referendum result would encourage support for a united Ireland.

Fianna Fáil's Micheál Martin said a border poll should be called, if there was evidence of sufficient support for it.