DUP wants an immediate return to Stormont
The DUP leader, Arlene Foster, proposed an immediate restoration of the assembly in Northern Ireland along with a parallel, time-limited process to deal with culture and language.
Mrs Foster described it as a "common-sense solution" to the ongoing political deadlock.
Sinn Féin rejected the plan and said the DUP have not addressed the cause of the assembly's collapse.
In June, talks between parties failed to restore a power-sharing executive.
At the DUP meeting in Belfast, Mrs Foster said if the parties fail to reach an agreement, then direct rule from London would be the only option.
Mrs Foster added that more talks would be a "waste of time unless there is some new thinking".
She said that the executive should be restored immediately so that ministers can deal with ongoing pressures in areas such as health and education.
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At the same time, she said, parties should "agree to bring forward legislation to address culture and language issues in Northern Ireland within a time-limited period to be agreed".
Mrs Foster warned that failure to do this "in a way that commands cross-community support" would lead to direct rule from London.
Mrs Foster acknowledged the need to deal with culture and language, but those matters "should not have a greater priority than health or education or the economy".
"We have nothing to fear from the Irish language nor is it any threat to the Union. However what we cannot and will not do is simply agree to one-sided demands," she said.
Mrs Foster also accused Sinn Féin of building "a barrier to the return of Stormont".
"I question whether Sinn Féin is serious about wanting to see an early return of Stormont. This is not an unreasonable question given some of the recent comments from Gerry Adams."
Sinn Féin's northern leader Michelle O'Neill rejected the DUP's plan.
Mrs O'Neill said the DUP proposal showed they have not acknowledged the reasons behind the collapse of the assembly.
"Establishing an executive that may collapse after a matter of months on the same issues will only fail all our people," she said.
Ulster Unionist leader Robin Swann acknowledged the DUP's proposal to restore the executive, but said that in light of Sinn Féin's "intransigence other options should be explored".
"If Sinn Féin and the DUP can no longer work together then other alternatives should be explored to ensure that Northern Ireland is governed by Northern Ireland politicians," he said.
The SDLP leader, Colum Eastwood, said the DUP proposition was a can-kicking exercise.
"Anything can be agreed in a time-limited parallel process can be agreed now. Time is not the issue, a critical lack of political generosity is."
Northern Ireland has been without a functioning devolved government since January, when the coalition led by the two biggest parties, the DUP and Sinn Féin, collapsed over a botched green energy scheme.
The late deputy first minister, Sinn Féin's Martin McGuinness, stood down in protest against the DUP's handling of an investigation into the scandal, in a move that triggered a snap election in March.
One of the major sticking points in talks to restore devolved government has been Sinn Féin's demand for an Irish Language Act.
Earlier this week, Sinn Féin president Gerry Adams said there would be no Northern Ireland Assembly without an Irish Language Act.
Stephen Farry described the ongoing deadlock as a "complete and utter mess".
The deputy Alliance leader told BBC's Good Morning Ulster programme both main parties had work to do.
"The DUP need to show a much stronger sense of realism about the depth of reasons as to why we're in the current crisis.
"At the same time, Sinn Féin need to show a little bit more in terms of flexibility and the speed of their rejection was telling of their attitude towards the talks."
He also told the programme it seemed "inevitable" there would be some sort of intervention from the UK government.
"We are seeing ever growing crises in terms of health and education. We have to have our own voice though and something that does reflect our circumstances here in Northern Ireland".