Sinn Fein leader Mary Lou McDonald has given an outright rejection to a proposal for a shadow Assembly to fill the gap until Stormont is restored.
And her deputy Michelle O'Neill said that Sinn Fein had no interest in a "Mickey Mouse" shadow Assembly to scrutinise decisions taken in Westminster.
Dublin TD Ms McDonald told an audience at Queen's University in Belfast last night that it was now up to the British and Irish governments to plot a course forward in the wake of the failed negotiations, as the DUP was "unable to deliver".
"For over 13 months we negotiated with the DUP, we reached an accommodation with their leadership," Ms McDonald said.
"The draft agreement, while not meeting all our proposals, presented progress and provided a basis to re-establish power- sharing.
"The DUP leadership were unable to deliver the draft agreement. I say this not to recriminate but to record my deep disappointment."
In the ongoing absence of devolution, the DUP has voiced support for a form of shadow Assembly, which would allow MLAs to scrutinise Cabinet decisions.
The Alliance Party has also proposed handing MLAs a role in examining the Government's handling of the region's affairs while the power-sharing crisis limps on.
Secretary of State Karen Bradley is examining the half-way house proposal as a potential means to govern Northern Ireland on an interim basis.
Ms McDonald said it is now "time to move on", but warned that a shadow Assembly was unacceptable.
"Any proposal for a shadow Assembly is not a move forward," she said. "It represents a step away from power-sharing. A shadow assembly would make us all bystanders to direct rule, giving a veneer of accountability to direct rule.
"Sinn Fein will not countenance direct rule.
"So, in order to re-establish genuine power-sharing, the two governments must convene the British-Irish Intergovernmental Conference.
"The Intergovernmental Conference must produce a plan, a pathway to bring forward the legislation and resources to secure these rights and implement the agreements."
Earlier, Ms O'Neill said Sinn Fein had no interest in scrutinising direct rule ministers.
"What we want is the institutions up and running again, what we want is the Executive up and running again and what we want is to be setting a programme for government and setting a budget, not focusing our efforts on some Mickey Mouse affair," she said.