Fine Gael leader Leo Varadkar has said that Fianna Fáil and Fine Gael would need a third party in order to form a government.
He said that the support of independents might also be needed.
Mr Varadkar said that any government that was formed would have to have a "functioning and working majority".
He said this would be necessary in order to make the kind of decisions over the "next couple of months and years to get the country going again".
Mr Varadkar said these decisions would not be easy or popular and that incentives or concessions to constituencies would not be made to convince people to come on board.
Earlier, Deputy Fine Gael leader Simon Coveney said it is possible to form a government quickly and he said Fianna Fáil and Fine Gael are working towards that.
Speaking in the Seanad as it debates emergency Covid-19 legislation, he called on others to play their part in forming a government saying "your country needs you".
Mr Coveney said his priority now was finding a way to work with others to find a government that can command a lasting majority.
He said Ireland needs a government that is strong, stable, diverse and one that can pass legislation at short notice.
Mr Coveney said the emergency Covid-19 legislation would be the most important ever passed in the house.
He said yesterday was the darkest day of the emergency so far for us, with 10 deaths.
Mr Coveney said we have to brace ourselves for a lot worse and said this "invisible enemy" was only beginning its spread through our country.
He said that while Brexit was a fight for citizens and livelihoods this is now a fight for citizens' lives.
He added we are being confronted with a once in a century crisis and he said the public expects politicians to do their jobs and to protect them.