Political parties in the North have been asked to participate in another round of talks in a bid to resolve the political crisis.
Secretary of State James Brokenshire has invited the parties to take part in the talks process at Stormont Castle on Monday.
The Irish and UK governments have said they want the talks to have an agreed agenda and regular round-table meetings.
A deadline to form a powersharing executive was missed on Monday.
However Mr Brokenshire has said he believed there was still a window of opportunity for parties to reach an agreement.
"The talks will have two objectives. First, to secure a coalition agreement to form the basis of the formation of a new Executive.
"Second, to address the implementation of outstanding issues from previous Agreements," said Mr Brokenshire.
He added: "In a shared approach, the UK government and Irish government have agreed this phase of talks will be best supported by an intensive process to drive progress."
He recently told MPs he does not believe there is an appetite for a fresh snap election.
Charlie Flanagan said that as a co-guarantor of the Good Friday Agreement, the Government "is determined to uphold its principles and protect its institutions".
He added: "In the days ahead we will work with all concerned to this end.
"I believe it is critically important to see devolved Government restored and working effectively in the interests of the people of Northern Ireland, in particular in the context of Brexit."
On Sunday talks to restore the institutions broke down after Sinn Fein said it would not nominate a deputy first minister.
Michelle O'Neill said at the time that talks to renew a powersharing agreement with the DUP had come to the "end of the road".
Responding to the invitation to attend another round of negotiations next week, Sinn Fein's John O'Dowd said the talks must be about the implementation of previous agreements.
He added: "There is a need to restore public confidence by securing political institutions based on equality, respect and integrity and delivering for everyone.
"That requires the British government and the DUP to commit to implementing the outstanding commitments of the Good Friday and subsequent agreements.
"The Irish government is a co-guarantor of the Good Friday Agreement and it must hold the British government to account.
"That will be Sinn Fein's focus in the talks."