Sinn Fein has rejected a compromise proposal by Arlene Foster on the Irish language and accused her party of not having learnt from the collapse of the last Stormont Executive.
The DUP leader last night offered an apparent olive branch to republicans with a pledge to legislate for the Irish language within a set period if power-sharing was restored.
She described it as "a common sense solution" that could break the political deadlock.
However, Sinn Fein's Stormont leader Michelle O'Neill dismissed it as inadequate while the SDLP said the proposal wasn't credible and described it as "missed opportunity".
Mrs Foster said: "I'm proposing that we restore an Executive immediately. Put ministers back into posts so that decisions can be made and that Northern Ireland can have a government again.
"But we also agree to bring forward legislation to address culture and language issues in Northern Ireland within a time-limited period to be agreed. If we fail to do that in a way that commands cross-community support then the Executive would cease to exist. This is an offer made in good faith with Northern Ireland and its people's best interest at heart."
Mrs Foster said that new talks would be "a waste of time unless there is some new thinking".
She warned that, without a deal, direct rule loomed.
The DUP leader said her party had "nothing to fear from the Irish language - nor is it any threat to the Union".
She continued: "Short-term patches or political expedience is not what is needed. I believe a new vision and a new commitment on identity is needed. We need to establish a new cultural deal to provide a comprehensive and long-term approach to the sensitive issue of identity."
However, Sinn Fein said that Martin McGuinness had been forced to resign because the DUP and the British Government hadn't honoured past agreements and operated power-sharing on the basis of equality.
Mrs O'Neill said: "The statement by the DUP leader demonstrates they have not listened or acknowledged the reasons of Martin's resignation. Establishing an Executive that may collapse after a matter of months on the same issues will only fail all our people. Let's agree to quickly conclude talks on implementation and rights, that is the only way to build a sustainable Executive that will last."
Ulster Unionist leader Robin Swann said that the speed of Sinn Fein's rejection of the DUP proposal "makes it abundantly clear that Gerry Adams' intransigence is still in place".
"In the meantime the future of our health service and lengthening waiting lists, our children and their education, and our small businesses are at stake. All these issues should trump political ideology," he said.
"If Sinn Fein 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."
SDLP leader Colum Eastwood branded the speech a "missed opportunity to show real leadership".
He insisted that there was nothing concrete in her speech to confirm she was offering an olive branch regarding an Irish Language Act.
He said: "If this is a signal towards a change of position from the DUP on a standalone Irish Language Act, then we welcome that, but there is nothing explicit in these remarks to confirm that yet. The proposals made are not a credible solution to the challenges we face, and the DUP leader knows that.
"They are the definition of kicking the can down the road."
Mr Eastwood said there was no point in restoring the Executive for it to collapse at a further stage, adding: "Anything that 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."
TUV leader Jim Allister said that Mrs Foster's speech showed "a lamentable failure to face the irrepressible reality that this Stormont is doomed to failure".
He insisted that Sinn Fein had no interest in making Northern Ireland work.
He said: "Pitifully, the leader of unionism begs for a return to the guaranteed failure of Stormont. Now, just a few months after recognising the dangers of crocodile feeding, she even offers to legislate for the promotion of the Irish language."