Sinn Fein's northern leader Michelle O'Neill said she is willing to find a resolution to Stormont's problems in post-election negotiations, but not if the Secretary of State is in the chair.
Mrs O'Neill said she wanted to see a return of devolved institutions that delivered for all citizens.
However, she reiterated her stance that James Brokenshire should not mediate any dialogue process that follows March's snap election.
If the DUP and Sinn Fein are again returned as the two largest parties, they will have only three weeks to resolve their differences and form a new power-sharing Executive.
Stormont could be facing a return to direct rule from Westminster if that deadline passes without a deal on issues such as legacy and the Irish language.
Mrs O'Neill and party colleagues met with Mr Brokenshire at Stormont House in Belfast to discuss the current political crisis yesterday.
After the meeting she said: "Sinn Fein will come at these negotiations with a willingness to find a way through to make sure we have institutions that deliver for all of our citizens. We have made it very clear and we repeat again that we will not return to the status quo."
Sinn Fein's Stormont leader accused Mr Brokenshire and the UK Government of favouring unionists.
"His one-sided partisan view means he cannot be an honest broker in negotiations," she said.
"I think the British Government have continually failed to live up to their responsibilities as co-guarantors of the Good Friday Agreement. They have pandered to unionism time and time again, and they have shown and demonstrated a one-sided approach when it comes to the issues of legacy." Mr Brokenshire travelled to Dublin yesterday evening for meetings with key political, business, energy sector and tourism figures to discuss the challenges facing Northern Ireland and the Republic as the UK prepares to leave the EU.
This morning the Northern Ireland Secretary is set to attend a business breakfast with Tourism Ireland ahead of scheduled meetings with Irish Foreign Minister Charlie Flanagan and Fianna Fail leader Micheal Martin.
Mr Brokenshire said he will discuss the current political instability with Mr Flanagan.
"My visit to Dublin comes at an important time, with the UK Government on course to trigger Article 50 by the end of March, which will begin our negotiations to exit the European Union," he said.
"As Secretary of State for Northern Ireland, I am acutely aware that the ability to move and trade freely across the border is an essential part of daily life for people and businesses on both sides of the border, and the UK Government recognises the importance of finding a practical solution that reflects the unique economic, social and political context of the border.
"We want to see trade and travel continuing to be as frictionless as possible.
"It is vital the Common Travel Area and excellent economic links with Ireland are maintained, and both issues will be significant priorities for the UK in the talks ahead.
"I also welcome the opportunity to meet Minister Flanagan to discuss the current period of political uncertainty in Northern Ireland and reinforce the commitment of both the UK and Irish governments to bring forward the bodies to address the legacy of Northern Ireland's past, as well as ensuring the establishment of a stable devolved government in a Northern Ireland that works for everyone."