The UK and Irish governments have warned time is running out for parties in Northern Ireland to restore devolution.
After a snap election radically altered the face of the Stormont Assembly - abolishing for the first time the overall unionist majority - political leaders have three weeks to form an executive.
But the two main parties - the Democratic Unionist Party and Irish republicans Sinn Fein - are on a collision course over Arlene Foster's leadership.
Sinn Fein have refused to pull back from its red line that the DUP leader can not be reinstated as First Minister while an inquiry is ongoing into alleged corruption and misuse of public money in a heating scheme scandal that forced last week's snap poll.
The DUP has insisted Sinn Fein can not dictate who they nominate to lead the party in any restored Stormont Executive.
In co-ordinated statements on Sunday, both London and Dublin called for urgent talks as there was a "limited window" to resolve differences and get a functioning parliament back up and running.
James Brokenshire, Secretary of State for Northern Ireland, said that responsibility lies on the shoulders of both the DUP and Sinn Fein.
"Now that Assembly members have been elected, there is a limited window in which the Assembly and Executive can be restored," he said.
"Urgent discussions need to take place to ensure inclusive devolved government resumes."
Mr Brokenshire added that "confidential" talks would start immediately to resolve other outstanding issues over the full implementation of peace agreements in the region and how the legacy of the Troubles is addressed.
Charlie Flanagan, Dublin's Foreign Affairs Minister, spent the morning talking by telephone to Mr Brokenshire and the main party leaders in Northern Ireland.
"Secretary of State Brokenshire and I agreed that it was of the utmost importance for the people of Northern Ireland that the political institutions, established under the Good Friday Agreement, promptly resume their work, not least so that they can effectively engage with the issues raised by Brexit," he said.
Mr Flanagan added: "In the coming weeks, we will work with all concerned to see the powersharing Assembly and Executive restored to effective and harmonious operation."
However, Sinn Fein's John O'Dowd, Education Minister in the last Executive, signalled a looming deadlock.
"If the DUP decide after the implementation talks that will take place over the next number of weeks that they are going to nominate Arlene Foster as joint First Minister, Sinn Fein will not support that nomination," he said.
"We were very clear on the doorsteps, we were very clear during the election and we have a mandate, and we said to people we would not support Arlene Foster as joint First Minister ahead of the publication of the RHI report."
Former Deputy First Minister Martin McGuinness collapsed the last Assembly by resigning over Arlene Foster's refusal to step aside pending an inquiry into the Renewable Heat Incentive (RHI) scheme.
The botched green energy initiative has been embroiled in controversy and could cost the Northern Ireland taxpayers £490 million.
An inquiry into its operation is not expected to make any findings for at least six months.
Mr O'Dowd said there is a "recipe for a stable executive and assembly" but warned the issues that forced the snap election could not be ignored.
"Alleged corruption at the heart of the government, alleged incompetence at the heart of government," he said, adding that the high turnout at the polls showed the public are "very, very tuned in" to the scandal.
But the DUP's Simon Hamilton, Economy Minister up until the assembly's collapse, said Ms Foster has a mandate to lead her party.
"We can't have the sort of powersharing John is talking about whenever you have diktats coming from Sinn Fein about who leads and who heads up the DUP in government," he told BBC's Sunday Politics.
"I have heard a lot from Sinn Fein over the last number of weeks about respect, but they are not respecting the mandate that the DUP has received, and that mandate endorsed Arlene Foster."
The pro-Brexit DUP narrowly remained the region's largest party by just one seat as a Sinn Fein surge saw the republican party make major gains over the DUP.
Having entered the election 10 seats ahead of Sinn Fein, the DUP's advantage was slashed to a solitary seat.
Only 1,168 first preference votes separate the DUP and Sinn Fein and, for the first time, Unionists will not have an overall majority at Stormont.
Amid the fallout, Mike Nesbitt said he would resign as Ulster Unionist leader.
Sinn Fein leader Gerry Adams has said the "perpetual unionist majority" at Stormont has been "demolished".