Talks aimed as restoring devolution will resume today - but with little hope of immediate progress.
And nationalists are set to press for returning Secretary of State James Brokenshire to be replaced by a more independent chairperson.
Sinn Fein president Gerry Adams said that if the DUP is "distracted" by propping up the Conservative government in London, the other parties could issue an invitation themselves.
And the SDLP also said they wanted an independent person appointed to oversee the negotiations as a result of the Conservative alliance with the DUP following the fallout from last week's General Election.
With less than three weeks to the deadline for the potential reintroduction of Direct Rule, expectations for the talks are already low and the General Election result has sparked further confusion.
The five main parties are all expected at Stormont Castle this morning, but it remains unclear whether a round-table session is even on the cards. But the deadline at the end of this month is more significant than the previous three, which Mr Brokenshire, who was reappointed yesterday, was able to deftly side-step to prevent the developing stalemate becoming a crisis.
At the start of July, spending cutbacks that are a direct result of the collapse of the Executive will begin to bite. Stormont will be working on only 95% of the budget it had last year, with Civil Service permanent secretaries forced to find new savings on top of the annual cuts most of the departments, apart from health, are having to implement.
After a phone call between PM Theresa May and retiring Taoiseach Enda Kenny yesterday, Downing Street said in a statement that the two premiers "confirmed their joint commitment to restoring a Northern Ireland Executive as soon as possible and agreed that both countries would continue to engage closely to bring about political stability in Northern Ireland".
The Prime Minister reiterated that the government's approach and objectives in the forthcoming talks to re-establish the Executive remained unchanged.
But SDLP MLA Nichola Mallon yesterday likened the situation to a workplace dispute in which the mediator was part of the company management. "How can you have a Secretary of State sitting as an honest broker when they already have a deal with one of the parties sitting around the table?" she asked on the BBC Sunday Politics show.
"It is just not possible to be neutral in this context, and anyone who pretends otherwise is ludicrous," the North Belfast MLA warned.
Mr Adams commented: "Sinn Fein has never accepted that the British government is impartial or neutral.
"The arrangements to restore the political institutions need not be protracted. The issues are well known, they are rooted in agreements already made, and the onus is clearly on the DUP to drop its opposition to the implementation of the rights-related issues which are at the core of the current difficulties.
"The pro-unionist and partisan nature of this British government has contributed directly to the current deep political crisis in the North.
"If the DUP don't prioritise the restoration of the institutions, and instead decide to become a prop for a dysfunctional minority government in London, then the parties should consider inviting an independent chairperson to oversee proceedings. Sinn Fein has already raised this at the beginning of the talks process some months ago."