James Brokenshire stays in hope of Stormont deal
Secretary of State James Brokenshire is expected to stay in Northern Ireland over the weekend in case there is any development in the political crisis.
Mr McGuinness, from Sinn Féin, quit as deputy first minister in protest at the DUP's handling of the botched Renewable Heat Incentive (RHI) scheme.
RHI is set to run £490m over budget.
On Thursday night, Sinn Féin members met in Londonderry where they heard calls for Mr Brokenshire and the Northern Ireland Office to move immediately to a fresh election.
Sinn Féin MLA Gerry Kelly told the meeting that the DUP's actions had undermined public confidence in the Stormont institutions.
Earlier on Thursday, Mr Brokenshire held talks with the political parties and Irish Minister for Foreign Affairs, Charlie Flanagan.
After the meetings, the secretary of state said "the clock is ticking down towards the start of next week" but admitted that a snap election was now "highly probable" as talks so far had failed to break the political deadlock.