Sinn Féin president Gerry Adams has said he does not expect a deal to restore powersharing to be struck by Monday.
He said the door was still open but there had been no sense of urgency around piecing together an agreement.
A series of deadlines have been missed to restore multi-party devolved government in Northern Ireland.
Mr Adams said: "I don't believe that there is going to be a deal by Monday.
"The DUP are showing no urgency or no real inclination to deal with the rights-based issues which are at the crux and the heart of these difficulties which we are talking here about."
He said those included republican demands for an Irish Language Act, a Bill of Rights, marriage equality and dealing with the legacy of decades of past violence.
"Unless they step-change I just cannot see, here we are on Saturday afternoon, I just cannot see how, and we told them this directly, how a deal can be put together by then."
The UK Government has extended the talks process until Monday, despite Stormont parties missing Thursday's deadline set in law.
Northern Ireland Secretary James Brokenshire will make a statement to the House of Commons on Monday outlining the Government's intentions going forward.
In the absence of agreement, the options open to Mr Brokenshire include setting another deadline for the talks process, calling a second snap Assembly election or re-imposing some form of direct rule from London.
The institutions imploded in January when DUP leader Arlene Foster was forced from office after Sinn Féin's then deputy first minister, the late Martin McGuinness, quit.
That was in protest at the DUP's handling of the renewable heat incentive (RHI), a scheme that left the administration facing a £490m overspend.
One of the main sticking points is over Sinn Féin's call for an act officially protecting the Irish language.
Republicans argue bestowing the status on the minority tongue would represent a major step towards respect and equality for all in Northern Ireland.
The DUP has said it already supported Irish medium school education during years of devolved government and has accused Sinn Féin of politicising its use.
Mr Adams attended a noisy and colourful equal marriage rally in Belfast city centre yesterday afternoon which attracted thousands of trade unionists, gay rights activists, students and supporters.
.@GerryAdamsSF and @moneillsf supporting the demand for marriage equality at a huge march and rally in Belfast today #EqualityMarch pic.twitter.com/q2MJhs6rcM— Sinn Féin (@sinnfeinireland) July 1, 2017
He added: "If there is a step change, part of that step change is for everybody to understand that equality and respect has to be at the heart of the institutions.
"They have to deliver for everybody, not just the Sinn Féin vote, not just the DUP vote, but for everybody including those people who don't vote, those people who are vulnerable, who are in poverty, who want their rights.
"There will be no return to the status quo, that is the only basis in which these institutions are going to be put together."
Mr Brokenshire told Q Radio he could see where areas of compromise may lie.
"But we are not there yet and time is running short," he said.
"There are no deadlines that I have set, I am simply making a statement to Parliament on Monday afternoon to update the House of Commons and to update on what the next steps might look like."