The parties have until Thursday to reach agreement
Talks aimed at restoring a power-sharing executive at Stormont in Northern Ireland will resume in Belfast later.
The parties have until Thursday to reach an agreement that would see the executive reactivated.
Foreign Affairs Minister Simon Coveney said he hopes the parties will have reached broad agreement by tonight.
"A functioning Executive and Assembly is in the best interests of the people of Northern Ireland. That is my focus and that of the Irish Government", Mr Coveney said.
Speaking on Monday, after reaching a minority government deal with the DUP, British Prime Minister Theresa May said: "Time is running short for the parties to come together and reach agreement to re-establish a power-sharing Executive by June 29th.
"I hope the parties will look beyond their differences and come together with a shared sense of common purpose to serve all communities in the best interests of Northern Ireland. Northern Ireland needs a functioning devolved government at this important time."
Mrs Foster also returned to Belfast from London for the discussions.
A former special advisor to Mrs Foster, Richard Bullick, is optimistic.
"The fallback position, in essence, is one of direct rule from London with the Conservative government propped up by the DUP where Sinn Féin have no say at all.
"I don't think that is a good outcome - and I still believe the DUP want to cut a deal in the next day or two and get things up and running again.
"So I think prospects have improved".