The DUP and Sinn Fein had been sharing power for nearly 10 years when the devolved government collapsed over a botched renewable energy scheme costing millions of pounds.
Northern Ireland Secretary of State James Brokenshire is to meet with the political parties later today, 04 September, to discuss restoring a power-sharing Executive.
Ms O'Neill however repeated her rejection of DUP leader Arlene Foster's call last week for the Northern Executive to be restored based on a commitment that the language issue would be addressed within a specific period of time, and that if it were not resolved the Stormont again would collapse.
Foster said that a series of "one-sided demands" by Sinn Fein had made progress impossible and that they must move to achieve a breakthrough.
She added: "I am not going to be prescriptive but we do not believe that there can be a prolonged set of talks".
Irish nationalists Sinn Fein must compromise if Northern Ireland is to avoid a "speedy" return to direct rule from London, the head of the Democratic Unionist Party said on Thursday. "We have no red lines".
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Sinn Féin Irish Language spokesperson Councillor Kevin Campbell has accused DUP MP Jeffrey Donaldson of "scraping the bottom of the barrel" in his opposition to an Irish Language Act.
"Given that it was the first time our community has held sustained power here since partition, nationalism in particular needs to reflect on that".
"We are not the barrier here to devolution in Northern Ireland".
She said, "We want to make the institutions work".
The political crisis in Northern Ireland looks set to continue as Sinn Fein have rejected the most recent offer from the DUP, created to return the parties to Stormont.