The Minister for Finance Paschal Donohoe has said it is "unlikely" that a new government will be formed by Easter.
Fianna Fáil and Fine Gael are engaged in talks to agree on a programme for government.
Last week, they issued a joint statement saying they have agreed the need to form a strong, stable government.
The statement added: "They are working to develop a programme for government that provides stability and a working majority in the Dáil."
However, they have both acknowledged that another party is needed to ensure a working majority.
Speaking on Newstalk's The Hard Shoulder this evening, Minister Donohoe said it would be a "very demanding" challenge to have a new government formed in the next two weeks.
He said: "If I look at the challenge I have now, if I look at the challenge we're going to have in containing this virus, we are going to need a majority government that can deal with the consequences of the emergency that we're now in.
"I'm certain that our country will get through this, I'm certain we will prevail.
"But I'm equally certain that in order to make some of the choices that will be needed to keep Ireland safe, to build on what we've done during the emergency, it will require a majority government.
"That majority government, in my view, has to have more political parties rather than Fine Gael and Fianna Fáil.
"We will do our bit with Fianna Fáil but we will need other political parties to reflect on where we are and decide if they want to play a role in forming a government for our country."
On the possibility of government formation talks being successfully completed in the next two weeks, Minister Donohoe said this was unlikely.
He said: "I just think given the imminence of April and the focus that everybody is putting into dealing with this virus, I think it will be unlikely it will be done by [Easter].
"But I think in the number of weeks after that, I think the larger two parties have to show they are able to come to some form an agreement but do that in a way that can be inclusive with a view to inviting other parties if they want to be part of it.
The Minister added that a stable, majority government will be needed in the coming months to deal with the impact of the coronavirus on the country and economy.
He said he hopes there will be an opportunity for all parties to consider that as Fianna Fáil and Fine Gael continue to engage with each other.