Fine Gael and Fianna Fail are meeting on Wednesday to discuss policy as efforts to form a government continue.
It is expected most of the talks will centre on the response to tackling the Covid-19 outbreak rather than significant policy discussions.
In a televised address to the country on St Patrick’s Day, Taoiseach Leo Varadkar said officials predict the number of cases of Covid-19 could reach 15,000 by the end of March.
If Fianna Fail and Fine Gael form a coalition, they still would not have the required number of seats.
They may need to rely on groups of Independent TDs because the Green Party which has eight seats, has refused to engage in government formation talks.
On Monday, they called instead for a “government of national unity” made up of all parties to address the pandemic.
On Sunday, Fianna Fail leader Micheal Martin said his party is ready to “step up” and form a government with Fine Gael to tackle Covid-19.
Mr Martin told Newstalk FM: “I am up for it, at moments such as this you have to step up to the plate and make sure a government with a majority is formed.
“My own view is that it needs to be expedited. The economic consequences of this, the big decisions that simply have to be taken, need a full government with all ministers accountable to the Dail.”
On Thursday, the Dail will return in a limited capacity to consider emergency legislation to give the Government powers to respond to the Covid-19 outbreak.
The measures would include the power to detain those believed to have the virus who refuse to self-isolate, and to direct people to stay in their homes.