Sinn Féin leader Mary Lou McDonald has suggested Fianna Fáil and Fine Gael may use the coronavirus outbreak "as cover" to go into government together.
Party leaders met yesterday afternoon for an update on the State response to the Covid-19 outbreak.
Meanwhile, Micheál Martin and Leo Varadkar met yesterday evening to discuss policy issues - with a second meeting scheduled for this morning.
It has led to increased speculation that formal government formation talks may start sooner than expected due to the coronavirus outbreak.
Speaking on Newstalk Breakfast, Deputy McDonald says a new government is needed - but it must be "reflective of the election" results.
She said: "In that regard, for Fianna Fáil and Fine Gael to go back into government together for the next number of years I think would run exactly against the grain of what the people told us.
"It may be in their minds to cobble together an arrangement - they may even use the fact that we're in a public health emergency as cover for them to go back into government together."
The Sinn Féin leader welcomed yesterday's meeting of party leaders.
They're now planning to meet twice a week, although Deputy McDonald suggested they might need to meet more regularly than that.
Noting the need for "united leadership", she said: "What I am saying very clearly is that where serious actions need to be taken speedily, obviously the caretaker government needs the involvement of the parties that have been returned in the recent election.
"Although Leo Varadkar is the Taoiseach, and although we do have a Cabinet and ministers, obviously they need to be doing more than simply briefing people like me.
"I don't want to be a spectator in this: I want to be part of delivering the solutions and ensuring that we protect our families and our communities, and that to me is what the leadership group is about."