Sinn Féin and the DUP have expressed a desire to restore powersharing in Northern Ireland but neither has signalled a softening of position in the Stormont standoff.
Democratic Unionist leader Arlene Foster and Sinn Féin's Stormont leader Michelle O'Neill used new year messages to reiterate their preference for devolved governance instead of a return to Westminster direct rule.
But they also made clear their stances on key sticking points in the long-running powersharing crisis had not changed.
It is almost a year since Northern Ireland had a properly functioning administration.
The institutions collapsed last January amid a row over a botched green energy scheme.
The rift between the DUP and Sinn Féin widened in the subsequent months.
A stand-off over proposed legislative protections for Irish language speakers and the North's ban on same-sex marriage are currently among the main sticking points.
Mrs Foster said the UK Government should move promptly to appoint direct rule ministers if a short final attempt at brokering a deal fails.
She said a short time frame should be set for renewed negotiations and rejected suggestions that the talks venue should be shifted to a hothouse format in England.
The former Stormont first minister said the continued absence of a devolved executive was "unacceptable and simply unsustainable".
"Recent rounds of talks have been bedevilled by the setting of pre-conditions by Sinn Féin," Mrs Foster claimed.
"Let us re-enter talks with one shared pre-condition - that we will redouble our efforts to restore devolution and start taking the decisions that the people of Northern Ireland so desperately need.
"Let's set ourselves a short time frame. And let's do it here at home rather than in some fancy English stately home."
Mrs O'Neill made clear Sinn Féin would only return to Stormont if the DUP was prepared to give ground on issues such as the Irish language and gay marriage.
"I want to lead Sinn Féin back into a new Executive because locally elected ministers are best placed to run local public services and fight back against the threats of Brexit and austerity," she said.
"I want to develop the widest possible consensus in political, civic and popular opinion to achieve this.
"I believe that can happen early in the new year but only if the institutions represent genuine and equal partnership government for all our people.
"That will require the British Government and the DUP accepting the political and democratic reality which has already been made abundantly clear by the electorate.
"If they continue to set their face against the people and against progressive politics, then there is an onus on the two governments (UK and Irish) to spell out how they intend to ensure the implementation of previous agreements and pave a pathway to restore the institutions on the basis of equal partnership and respect in the terms set out almost 20 years ago."
Mrs Foster said: "I still believe that the best way to deal with the issues facing our society is for Stormont to be back up and running with locally elected and accountable politicians taking decisions on the issues that matter to people across our province.
"A return to direct rule would be an inferior alternative, but it would be a government.
"But the people of Northern Ireland deserve a government and if Sinn Féin persist with their intransigence then the Secretary of State (James Brokenshire) should move to appoint direct rule ministers early in the new year."
Mrs O'Neill said she was "optimistic" that powersharing could be put back together.
"I am optimistic because I see the transformation that has taken place in this society since the people voted for the Good Friday Agreement 20 years ago," she said.
SDLP leader Colum Eastwood insisted direct rule was not inevitable.
He accused Sinn Féin and the DUP of overseeing 10 years of failed governance.
"British direct rule can't, like Brexit, be enforced upon us," he said.
"Instead of being led into the easy comfort of our own silos, let all of us in political life finally reach for solutions.
"Whether from a nationalist or unionist tradition, each and every one of us belongs to this small corner of Ireland.
"Our only choice is to live with each other and work together."