Taoiseach Leo Varadkar has said he is optimistic a deal on restoring power-sharing in Northern Ireland will be done by the 29 June deadline.

Speaking on RTÉ’s Six One after talks with Sinn Féin and the DUP at Government Buildings, Mr Varadkar said he will travel to London early next week to meet British Prime Minister Theresa May to discuss the Irish and British Government’s renewed commitment to ensure the Stormont Executive and Assembly is re-established before the 29 June deadline.

The Taoiseach said he will also discuss Brexit with Mrs May.

Mr Varadkar said: "People in Northern Ireland have voted for a devolved government; they want to be governed from Stormont and it's important that happens.

"It's really important for all of the island of Ireland that Northern Ireland has an executive in place and has a unique voice because we are now entering into Brexit negotiations and there's a lot that unites us across the island when it comes to Brexit and the type of Brexit that might work for us."

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Mr Varadkar said he hoped to see a united Ireland in his lifetime, but he was conscious of the current agreement of "an agreed Ireland" and the Good Friday Agreement.

He said if there's to be any change to the constitutional position of Northern Ireland, it is important that there is a strong consensus in favour of that, both in the Republic and in Northern Ireland.

Mr Varadkar said he did not foresee a Fine Gael coalition arrangement with Sinn Féin, saying "we are not compatible", but added it is important to recognise that what happens in Northern Ireland is different.

Earlier, DUP leader Arlene Foster said she thinks it is "very realistic" that a deal can be reached on power-sharing by the end of June.

Speaking outside Government Buildings after meeting Mr Varadkar, Mrs Foster said: "The issues that have to be dealt with have been talked about now for quite a period of time.

"We have been out of office now since January, we then had the March election, we had a series of negotiations after that, then the general election came.

"So I think it is very much doable to have a deal by the end of this month."

She said it was down to Sinn Fein whether an agreement is done.

"It takes two to tango and we're ready to dance," she said.

Mrs Foster added that "we will go into speak with Sinn Féin again on Monday morning" because devolution works and "works for everybody in Northern Ireland."

The DUP, under Mrs Foster, has not yet struck a deal with the Conservatives that would allow a beleaguered Theresa May form a minority government in London. 

Sinn Fein Stormont leader Michelle O'Neill voiced her optimism that a deal on Stormont was "doable".

"We remain fully committed to making the institutions work," she said.

"We also respect the other parties' mandates, we want to get back to an executive that has all the parties around the table to collectively take decisions.

"I think it is all very doable."

Sinn Féin President Gerry Adams led the delegation to meet Mr Varadkar including Ms O'Neill, Sinn Féin deputy leader Mary Lou McDonald and newly-elected Fermanagh South Tyrone MP Michelle Gildernew.

Mr Adams said they would be pushing Mr Varadkar to raise the prospect of a border poll on Irish reunification within the next five years in discussions with the British government.

On his talks in London with Prime Minister Theresa May on Thursday, he said they had offered an "Irish solution to an English problem" as giving Northern Ireland special EU status after Brexit to keep an open border on the island.

"We made the case to her that we would oppose any deal that undermined the Good Friday Agreement," he said.