"We will go into speak with Sinn Féin again on Monday morning to try and get that set up as quickly as possible, because devolution works and works for everybody in Northern Ireland".
Talks are still ongoing between the Prime Minister and Mrs Foster, although no agreement is expected to be reached until next week.
"I think it is very much doable to have a deal by the end of this month", she added.
Taoiseach, Leo Varadker will hold separate meetings with the DUP and Sinn Féin leaderships in Dublin today.
"We remain fully committed to making the institutions work", she said.
"I want us to have a good working relationship so that from his jurisdiction and my jurisdiction we can work together for the good of all our people", she added.
Gerry Adams led a delegation to Government Buildings including Ms O'Neill, Sinn Fein deputy leader Mary Lou McDonald and newly-elected Fermanagh South Tyrone MP Michelle Gildernew.
He confirmed they had also discussed the possibility of a referendum on Irish unity.
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Fultz was one of eight National Basketball Association prospects to workout for the Sixers in Philadelphia on Saturday. He's giving me tips and pointers and he's pretty amusing , so when I saw that it was pretty cool and pretty amusing .
However, putting the pro-British unionist DUP in a position of influence in London could also undermine the British government's ability, enshrined in a 1998 peace agreement, to function as an impartial broker between Northern Ireland's unionists and its Catholic Irish nationalists.
"There is an irony to being lectured about our role in terms of the national government of the United Kingdom when Sinn Féin wants to be in government here in the Republic of Ireland".
"What would happen then?"
Things have moved on a bit since then with Brexit, but we do know they're looking at trying to lower the cost to the Northern Ireland Executive of any move on corporation tax.
A Conservative source said there was so far no deal to announce and that a decision on the timing of any announcement would have to wait until an agreement was finalised.
In a statement to reporters outside afterwards, Mr Adams said: "We told her very directly that she was in breach of the Good Friday Agreement, and we itemised those matters in which she was in default in relation to that agreement".
"We know each other and we understand each other", she said.
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