Sinn Féin has rejected a DUP bid to restore the Assembly and resolve division over cultural issues.
Republican leader Michelle O'Neill said establishing a powersharing administration that may collapse after a matter of months on the same issues would only fail the people.
Democratic Unionist chief Arlene Foster called for a "common sense" solution appointing Stormont ministers alongside a time-limited process for making progress on the red line issue of an Irish language act and Ulster Scots.
Unless proposed laws enjoyed cross-community support the troubled institutions would fall yet again, she said.
Foreign Affairs minister Simon Coveney said Mrs Foster's intervention was: "A genuine effort to show leadership and reach out towards compromise."
Mrs O'Neill said: "The statement by the DUP leader demonstrates that they have not listened or acknowledged the reasons of Martin (McGuinness)'s resignation.
"Establishing an Executive that may collapse after a matter of months on the same issues will only fail all our people.
"Let's agree to quickly conclude talks on implementation and rights, that is the only way to build a sustainable Executive that will last."
Powersharing has been suspended since early this year when late Sinn Féin deputy first minister Mr McGuinness resigned in protest at the DUP's handling of a botched green energy scheme which risks landing the taxpayer in millions of pounds of debt.
Talks aimed at restoring the institutions are due to resume on Monday led by the Irish and British governments, with some prominent DUP MPs warning a return to direct rule from Westminster could be looming.