Prime Minister David Cameron and Taoiseach Enda Kenny have urged Stormont's politicians to strive for agreement as the on-going talks process enters a crucial phase.
The two leaders both acknowledged major issues remain unresolved in the negotiations between the five Executive parties but expressed hope progress could be achieved.
Their statements came as former US Senator Gary Hart returned to Northern Ireland, to add his weight to efforts to break the deadlock.
While no formal deadline has been set to reach agreement, Christmas is seen by many as an effective cut-off point.
The talks are centred on resolving long-standing impasses over the issues of flags, parades and how Northern Ireland deals with its violent past.
The future of the Assembly and its failure to implement Westminster welfare reforms is also being negotiated.
Mr Cameron and Mr Kenny are due to travel to the province before Christmas.
"Clearly these are complex and difficult issues, and I recognise the scale of the task that lies ahead," said the Prime Minister.
"The UK Government will do all it can to support the parties in their efforts to reach agreement, and I am satisfied that we have done so thus far.
"I urge the parties to continue in their endeavours and look forward to a further report on progress in the near future."
Mr Kenny warned the parties that the window is narrowing for a deal.
"I recognise that complex and difficult issues remain to be addressed," he said. "However, politics - and political leaders - have to now focus on delivering an agreement for all the people, even if that requires difficult negotiation and compromise."