The Irish and British governments have met Northern Ireland's main party political leaders in Belfast to see if a basis exists for agreement any time soon on restoring power-sharing at Stormont.
After dissident republicans shot and killed journalist Lyra McKee during rioting in Derry on 18 April, the political vacuum in Northern Ireland came under scrutiny.
In their role as guarantors of the Good Friday Agreement, the Irish and British governments convened talks involving the five main Stormont parties.
They have met in working group formats a number of times since, discussing issues that were a factor in the collapse of power-sharing in January 2017.
The interactions were said to be positive, but so far no solid agreement proposals have emerged.
DUP leader Arlene Foster said the party was "constructively engaging" in the talks.
"I very much hope that we can continue in the constructive way that we have been engaging and we can find a way forward," she said.
"We are up for finding a way forward as quickly as possible. It has to be a balanced way forward and one that everyone in society can sign up to."
A joint statement issued last night by Taoiseach Leo Varadkar and British Prime Minister Theresa May urged the parties to intensify their discussions.
Tánaiste and Minister for Foreign Affairs Simon Coveney and Northern Ireland Secretary Karen Bradley met the parties at Stormont today.
The broad plan is to see if they can work up the basis for an agreement over the next few weeks.
While the odds are against a deal, nobody wants to be identified as the cause of failure.
Sinn Féin has urged leaders in Northern Ireland to show political will despite the "improbable" circumstances, and seal a deal on restoring power-sharing.
The party’s leader Michelle O'Neill said: "It is very reasonable, the public deserve an Assembly and Executive, one that functions well, one that serves them well, one that looks after all in society.
"We are determined to try and achieve that, so what is required in this space is political will.
"We have political will, we are willing to discuss and to talk with the other parties.
"What we are asking for is absolutely reasonable, previous agreements to be implemented, equality and respect for all citizens, integrity in government."
Additional reporting PA