Leo Varadkar has said Fine Gael and Fianna Fail are close to reaching a programme for government and will start approaching smaller parties.
The two negotiating teams are meeting again today to discuss policies for a possible programme for government.
Progress on forming a government has been slow since the general election on February 8.
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Mr Varadkar has said he remains opposed to going into government with Sinn Fein, even though the republican party obtained the largest number of first preference votes in the general election.
Before the coronavirus outbreak, Sinn Fein held several public meetings to rally public support for its efforts to get into government in the Republic.
Speaking in Dublin today, the Taoiseach said: "There are discussions under way with Fianna Fail at the moment and we hope that either this week or next week to agree a joint document with them and that would allow us to approach third parties like the Greens, Social Democrats and Labour.
"We are a few weeks away and people are working on it but I also think people understand that the number one priority for all of us at the minute is dealing with Covid-19.
Mr Varadkar said the current caretaker government has no requirement to pass any legislation.
"However that is an issue that could arise in the coming weeks," he said.
"When the election happened a few months ago, it was my party's view that we should enter opposition. We stepped back and allowed other parties to try and form a government.
"They were not successful and as a result of that we have now stepped in to try and work with other parties to form a government."
Asked if he thinks he will still be Taoiseach next month, he said: "Obviously that is something that is up for discussion with Fianna Fail but they are a party who have slightly more seats than us and we recognise that.
"I don't think anyone's focus is on what jobs they are going to hold in a week's time or a month's time. My focus is on dealing with this public health emergency and minimising the economic damage and ensuring our society and economy can bounce back."
