Michelle O'Neill says "today we have come to the end of the road."
Sinn Fein president Gerry Adams said he does not believe it will be possible for them to reach agreement with other parties before Monday's 4pm deadline.
Its leader at Stormont, Michelle O'Neill, said the republican party will not be nominating a deputy first minister.
She said: "Today we have come to the end of the road.
"The talks process has run its course and Sinn Fein will not be nominating for the position of speaker or for the executive office tomorrow."
Speaking from Stormont Castle, Minister for Foreign Affairs and Trade, Charlie Flanagan stated: "“This is a critical time for Northern Ireland. We are on the cusp of the triggering of Article 50 by the UK Government.
"It is the strong wish of the Irish Government to see power-sharing re-established so that the interests of the people in Northern Ireland are best protected and advanced.
"I therefore urge the parties to avail of the remaining time available to re-engage on the few outstanding issues that divide them."
Power-sharing collapsed in January after a row over a botched green energy scheme predicted to cost the taxpayer up to half a billion pounds.
Sinn Fein has said it will not share power with the Democratic Unionists' leader Arlene Foster as first minister until a public inquiry into the renewable heat incentive (RHI) is concluded.
SDLP Leader Colum Eastwood has said the collapse of the all-party talks was not solely due to RHI, but about how people and communities were treated, and that "those who are responsible for creating that poisoned political atmosphere must address it in word and action.
He said that those who voted earlier this month will now by very angry and they "are right to be."
Mr Eastwood also called on the Secretary of State to "create space for all parties to refresh their outlook on the challenges we face and reach a positive accommodation that allows a restoration of power sharing.”
DUP leader Arlene Foster said a statement this evening that "negotiations will only ever be successful when parties are prepared to be flexible in order to secure outcomes. To date there was little to suggest that Sinn Fein want to secure agreement.
"Throughout the course of Saturday Sinn Fein behaved as if they were the only participants whose mandate mattered. This cannot and will not be the basis for a successful outcome.
"The DUP stands ready to continue to discuss how we can secure new arrangements for Northern Ireland."
Monday is the deadline for nominating a first and deputy first minister at Stormont or else Northern Ireland Secretary James Brokenshire is obliged to intervene.
Fresh elections or direct rule from Westminster could be imposed within a reasonable period.