James Brokenshire has warned that the "need for intervention is becoming increasingly clear"
Simon Coveney says Northern Ireland's political crisis "is not sustainable for many more weeks".
The Minister for Foreign Affairs spent the day meeting with Stormont's main parties, looking at how the talks should continue.
The North has been without an Executive since the Stormont Assembly collapsed in January.
Talks between the DUP, Sinn Féin and various smaller parties got underway after the election in March, but so far no agreement has been reached to restore power-sharing.
The UK's Northern Secretary James Brokenshire was in Belfast yesterday as part of the ongoing efforts to break a deadlock between Sinn Féin and the DUP.
Mr Brokenshire has warned: "The window of opportunity to restore devolution and form an Executive is closing rapidly as we move further into the autumn.
"The need for intervention is becoming increasingly clear."
Today, Minister Coveney told leaders they need to "trust" each other if they are to restore power-sharing.
Speaking to reporters, he observed: "There is a need for a deal to be done between Sinn Féin and the DUP on some core issues that divide them at the moment.
"We need to find a way of doing that allows the leadership of both parties to be able to sell that to their support base."
He said that decisions around issues such as healthcare, Brexit and responses to recent flooding "need political leadership in place" - but added that is currently "not there":
Over the weekend, the Foreign Affairs Minister praised the DUP leader Arlene Foster for 'making a real effort' to resolve the impasse in Northern Ireland.
Arlene Foster has said she is prepared to do a deal on key issues like the Irish language, once power-sharing resumes.
Sinn Féin, however, has rejected the idea.