Sinn Féin has said it is not prepared to accept a deal to save Stormont at "any price".
The party resumed negotiations with the DUP this morning in a bid to restore the power-sharing government following the extension of yesterday's deadline.
Talks between the two parties adjourned earlier this evening and are to resume tomorrow morning.
It is understood that no significant progress was made in today's series of meetings.
Sinn Féin negotiator Conor Murphy has insisted that they stand firm over the issue of rights for all citizens, including language, legacy and gay marriage.
Referring to the SDLP, he challenged critics of the party to say if they want a deal "at any price".
Mr Murphy added that this is a "very key time" in the talks process with the DUP.
"The people who are criticising us for standing firm in these negotiations need to explain what they mean by 'get a deal at any price'," said Mr Murphy.
"For our part in Sinn Féin we are here engaged, not on party political interests but actually on issues that are rights for people who support us and for many, many people who don't support us.
"We are here to protect people's rights and ensure that any legislation which is put back in place is done so on the basis of the Good Friday Agreement."
Mr Murphy also said that if Northern Secretary James Brokenshire decides to legislate for a budget for the region at Westminster, "this phase of the talks process is over".
He also admitted there is a "credibility issue" the longer the talks drag on.
Minister for Foreign Affairs Minister Simon Coveney and Mr Brokenshire arrived back at Stormont today in a bid to help break the political deadlock.
They said progress was made yesterday between the DUP and Sinn Féin during talks aimed at restoring power-sharing.
Both men and the parties arrived back at Stormont this morning to resume discussions after a late night of negotiations.
Read more - Deadlines and other Stormont questions
Mr Coveney tweeted that "everyone (is) working hard to get a deal across the line".
Mr Brokenshire has extended the deadline for the parties to reach agreement and will review the situation tonight.
They were warned Mr Brokenshire they had until yesterday to produce a written agreement or he would be forced to legislate for a budget for the region at Westminster.
However he decided last night that the parties had made progress and he was going to defer his decision.
In a statement he said: "The parties have made further progress during the course of (Monday).
"They are making certain additional requests of the UK Government which we need to consider.
"In the light of this, I believe it is right to defer the assessment on whether to introduce legislation to Parliament this week to enable an Executive to be formed.
"The parties will recommence talks in the morning (Tuesday) and I will reassess the position (on Tuesday) night."
Former secretary of state for Northern Ireland Peter Hain has said the impasse in the region is bringing great disillusionment and cynicism.
He said that it is not healthy for democracy, not healthy for the Good Friday Agreement and he worries deeply about it.
Speaking on RTÉ's Drivetime, he said if he were secretary of state, he would make it clear to politicians in Northern Ireland that they cannot continue to draw their salary, expenses, staffing allowances and direct party funding for "not doing their jobs", adding it has become a soap opera.
He said there is a limbo in Northern Ireland, where people have no government and it is not clear to him what the solution is.
The Northern Ireland Executive collapsed in January and the region has been without a power-sharing government since then.
Despite endless rounds of discussions, a deal to restore devolution has proved elusive, with the introduction of an Irish language act seen as the main issue.
