Sinn Fein’s Northern Ireland leader said she “wants to give hope to people” that a solution to the current deadlock can be found.
“I believe this can be done, but it can only be done if there is political will there,” she said; the reason for the failure “firmly falls at the feet of the DUP”.
She added: “At the heart of the Good Friday Agreement was mutual respect and parity of esteem and that was a principle which the DUP have failed to take on board and look after all the citizens we’re elected to look after.
“They’ve continued to block people’s rights, whether that be marriage rights, legacy inquest rights, whether that be language rights,” she told the BBC’s Sunday Politics programme.
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The Stormont Executive collapsed in January after Martin McGuinness resigned as deputy first minister, claiming that the DUP had undermined power-sharing and mishandled the RHI crisis.
But the DUP’s Simon Hamilton said that Ms O’Neill was merely engaged in political “posturing”.
Her comments come little more than a month after she declared that devolution talks “are over”, he said.
“It’s time Sinn Fein got real. They collapsed Stormont for selfish political reasons and pulled down talks when their shopping list wasn’t being advanced.”
The problems facing the education and health service are well known, he said, but Sinn Fein is prioritising them below an Irish language act.
“Sinn Fein’s own electorate, like everyone else, are suffering as a result of the posturing by republicans. If Sinn Fein truly are serious about restoring devolution then they’d be re-engaging in talks rather than engage in white-line pickets and press releases.”
UUP negotiator Doug Beattie said that Mrs O’Neill may be trying to attempt “some deflection in advance of Christmas” but that the unfortunate reality is that “nothing has changed”.
He added: “The weekend comments from Michelle O’Neill represent little more than yet further strategising from Sinn Fein in an attempt to build up a narrative in the eyes of the electorate which says that Michelle O’Neill and Gerry Adams are not responsible for the ongoing political impasse.”
Sinn Fein shows no signs of being open to all-party talks or to discussing where they got to in talks with the DUP.
“They expect unionism to capitulate in a back door seedy deal which we in the Ulster Unionist Party will not do. And they still won’t discuss governance issues with all parties.”
Mick Fealty, editor of the Slugger O’Toole political blog, said Mrs O’Neill has a “no-compromises-on-anything pitch, [which] like previous stand offs, allows Sinn Fein to keep ‘negotiating’ until trouble has passed”.
Regarding Sinn Fein’s demands on human rights and same-sex marriage, he said “the proper place for such decisions is through the elected voice of the people of Northern Ireland, ie the Assembly.
“Nowhere in the western world are such important matters taken above the heads of the people and settled in secret negotiations behind closed doors.”
Both issues could have been resolved by amending the Assembly petition of concern mechanism – which Sinn Fein refuses to do, he added.
Kenny Donaldson of Innocent Victims United said Sinn Fein’s demand for legacy inquests must not be met until there are structures to address “the access to justice deficit experienced by victims of terrorism”.