Mary Lou McDonald has insisted that a return to direct rule from London "is not an option"
Sinn Féin's new leaders will meet with the Taoiseach and Tánaiste in Dublin later today.
Leo Varadkar says he wants to hear Sinn Féin's assessment of the events of last week, and the collapse of power-sharing talks at Stormont.
DUP leader Arlene Foster announced last Wednesday that negotiations had been unsuccessful, highlighting issues around the Irish language as a particular sticking point in talks.
Mrs Foster said she has asked the British government to set a budget for Northern Ireland and start making policy decisions about "schools, hospitals and infrastructure".
Sinn Féin, meanwhile, blamed the DUP for collapsing the talks, insisting that the two parties had "achieved an accommodation across the issues involved".
Today, the Taoiseach wants to gauge the prospect for an early resumption of negotiations between Sinn Féin and the DUP.
He is expected to emphasise that, despite the disappointment surrounding the decision to halt the talks, the only way forward is dialogue and compromise between the two parties.
Speaking ahead of the talks, Sinn Féin leader Mary Lou McDonald said she is also due to meet with Theresa May this week.
She said: “Michelle [O'Neill] and I will be telling the Taoiseach and the British Prime Minister it is the responsibility of the two governments to implement the agreements on legacy and an Irish Language Act and to provide for marriage equality.
“We will also make it clear to both government that a return to direct rule from London is not an option. Sinn Féin remains committed to working for an agreement. However, any return to talks must be progressive and ultimately they must deliver for citizens.”
The latest round of talks were the latest attempt to resolve an almost year-long struggle to restore power-sharing at Stormont, with several rounds of negotiations since elections last March.
Northern Ireland has been without a power-sharing government since the collapse of the Stormont Executive in January 2017, amid a scandal over a botched renewable heat scheme.
Reporting by Sean Defoe and Stephen McNeice