Stormont party chiefs will meet Northern Ireland Secretary James Brokenshire later for preliminary talks on finding a way to restore devolution, it is understood.
Following the major shake-up of the snap election, leaders have three weeks to form an executive or risk the re-imposition of direct rule from Westminster.
The two main parties, the Democratic Unionist Party and Irish republicans Sinn Fein, are on collision course over Arlene Foster's leadership.
Sinn Fein has refused to pull back from its red line that the DUP leader cannot be reinstated as first minister while an inquiry continues 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 cannot dictate who they nominate to lead the party in any restored Stormont Executive.
On Sunday, Theresa May and Enda Kenny ordered ministers to open urgent negotiations with the parties after the poll radically altered the face of the Stormont Assembly, ending for the first time the overall unionist majority.
The two leaders agreed to discuss the issue again at the EU council summit in Brussels on Thursday.
It is understood Mr Brokenshire will meet all five main party leaders on Monday "on a bilateral basis", ahead of talks including Irish Foreign Minister Charlie Flanagan on Wednesday.
In separate co-ordinated statements on Sunday, Mr Brokenshire and Mr Flanagan warned there was a "limited window" to resolve differences and get a functioning parliament back up and running.
Mr Brokenshire said responsibility lies on the shoulders of the DUP and Sinn Fein.
He added that "confidential" talks would start immediately to resolve other outstanding issues over the full implementation of peace agreements and how the legacy of the Troubles is addressed.
Mr Flanagan said it was of the utmost importance for the people of Northern Ireland that the political institutions, established under the Good Friday Agreement, promptly resume, "not least so that they can effectively engage with the issues raised by Brexit".
However, on Sunday Sinn Fein's John O'Dowd, education minister in a previous executive, said Sinn Fein would not support Ms Foster's nomination.
The DUP's Simon Hamilton, economy minister until the Assembly's collapse, said Ms Foster has a mandate to lead her party.
Former deputy first minister Martin McGuinness collapsed the last Assembly by resigning over Ms 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 Northern Ireland taxpayers £490 million.
An inquiry into its operation is not expected to make any findings for at least six months.
The pro-Brexit DUP narrowly remained the region's largest party by one seat as a Sinn Fein surge saw the republican party make major gains on the DUP.
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.
On Sunday, Sinn Fein president Gerry Adams took aim at the Conservative Government in London, saying it is "part of the problem" of the political crisis in Northern Ireland, accusing No 10 of seeking to impose Brexit and refusing to implement agreements on the legacy of the Troubles.
But the Sinn Fein leader said his party will be at Stormont on Monday to "engage positively with all the other parties" to find a way forward.