Update 1.40pm: The DUP leader Arlene Foster has been meeting with the new Taoiseach in Dublin.
The former First Minister became the first political leader to meet Leo Varadkar in Government Buildings, in a 45-minute meeting.
Arlene Foster answers questions outside Government buildings after meeting with Taoiseach Leo Varadkar this morning. pic.twitter.com/SRdQpLpnJh— RTÉ News (@rtenews) June 16, 2017
The two discussed the ongoing talks to restore power-sharing in Northern Ireland, and the DUP's new role in Westminster.
Afterwards Ms Foster told reporters she was confident that the DUP and Sinn Féin could overcome their differences to share power together.
“It takes two to tango, we’re ready to dance - it is up to others to decide otherwise. We have been out of the office now since January, we then had the March elections. We had a series of negotiation 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.”
Earlier: New Taoiseach Leo Varadkar will meet the North's two main political parties later.
Sinn Féin and the DUP will come to Dublin for talks about power-sharing.
Both sides met with the British Prime Minister yesterday, amid fears that a DUP deal with Conservatives in Westminster could unbalance the peace process.
The deadline for a Stormont deal is June 29.
Meanwhile, talks are also continuing between the Conservatives and the DUP on the potential Westminster deal.
Theresa May needs the 10 DUP MPs to govern without a majority after her gamble on a snap election backfired.
It is understood there's "broad agreement" on the principles of the Queen's Speech - now due on Wednesday - which will set out the government's plans.