Enda Kenny and Micheal Martin spoke by phone last night after their negotiating teams adjourned talks over several sticking points.
The main issue is water charges, although housing, education and rural affairs are also causing problems.
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If the two leaders can agree a way forward, they will mandate their negotiators to resume talks.
Speaking after the talks at Trinity College Dublin yesterday Fine Gael negotiator Paschal Donohoe said there was determination to reach agreement.