Sinn Féin has rejected Arlene Foster's latest offer to break the political impasse in Northern Ireland.
The DUP leader wants a twin-track approach where the devolved institutions are restored quickly to deal with issues like running the health service, while a separate process addresses disagreements like that over same-sex marriage.
On Wednesday, Catholic peacemaking priest Fr Martin Magill challenged politicians as to why it had taken the death of 29-year-old Lyra McKee to unite them, at her funeral.
Sinn Féin deputy leader Michelle O'Neill said on Thursday: "In terms of what Arlene Foster has proposed today, in terms of going into the Executive and having a parallel process, that will not work.
"The citizens here deserve to have their rights delivered on, marriage equality, language rights, legacy inquest rights.
"These things need to be delivered, and that in itself then paves the way for the institutions to be restored."
The Northern Ireland Assembly and ministerial Executive collapsed more than two years ago in a row between the former power-sharing partners over a botched green energy scheme.
Sinn Féin leader Mary-Lou McDonald has said her party is ready to play a full part in a "serious and meaningful" talks process aimed at restoration.
Her party is seeking guarantees around the place of the Irish language and changes to the law on same-sex marriage.
The DUP has consistently called for devolution to be revived or for the UK Government to step in to make more decisions.
Northern Ireland Secretary Karen Bradley has said she intends to hold discussions with Stormont's party leaders.
They attended a vigil together in Londonderry after Miss McKee was shot dead by dissident republicans.
In response to Michelle O'Neill's comments, Ms Foster said she was disappointed but “not entirely surprised”.
“I had hoped the atmosphere of yesterday and indeed since Lyra McKee was murdered might have encouraged her to look proactively at getting back into the Assembly because that’s what people want,” she said.
“We fundamentally believe that the Assembly needs to be up and running and ministers need to be taking all of those decisions and let’s be clear, there will be difficult decisions to take in relation to moving forward in Northern Ireland but we’re up for that and we’re up for having the assembly up and running again.
She continued: “But let’s have a talks process where we can agree a balanced deal for all of the people of Northern Ireland so that everybody feels ownership of the Assembly and of what we’re doing there.”
Speaking about Fr Magill’s challenge to politicians, Ms Foster added: “He had a very clear message for us, I said to him when I spoke to him on the phone to say I am not going to be found wanting in wanting to get the assembly up and running. I want it up and running now.”
At Stormont on Thursday afternoon SDLP leader Colum Eastwood made a proposal which he says could see power-sharing restored.
Mr Eastwood said suspending the petition of concern (POC) mechanism can allow power-sharing government to resume.
He told reporters that he has spoken to Irish Foreign Minister Simon Coveney about the proposal and plans to have a conversation with Northern Ireland Secretary Karen Bradley later.
"Today, the SDLP is proposing the suspension of the Petition of Concern mechanism for the remainder of this Assembly in order to legislate for rights and for all of our futures through the democratic mandate handed to us by the people of Northern Ireland," he said.
"We are also proposing that while the temporary suspension takes place, a meaningful review of the POC is conducted with experts to find agreement on how to protect rights and stop any future abuse of the mechanism. The SDLP has the legislation ready to bring progress and equality - we can begin to enact it on the Assembly's very first day back.
"This proposal threatens no-one. It is about creating the space to get parties back into Stormont to take decisions affecting all of our lives. It is clear there is an Assembly majority to resolve the outstanding issues if we remove the veto. We need to bring our people back together, we need to bring our government back together. This is a time for leadership, for courage and for compromise."