Negotiators from the centre-right Fine Gael party are to sit down with Labour representatives later today in round one of the complex talks.
Both sides accept they are under pressure from Europe to strike a deal by the end of the week.
Enda Kenny, who led Fine Gael to an historic success at the polls at the weekend, is to finalise his negotiation team mid-morning.
He has already made contact with Labour leader Eamon Gilmore to tee up what could be several days of tough discussions.
Depending on the numbers, Mr Kenny may also have the option of forming a coalition with like-minded independents.
A spokesman for Fine Gael said initial contacts have been made to open negotiations on a programme for government.
"Enda Kenny will be appointing a negotiation team this morning," he said.
"There was initial contact between Mr Kenny and Eamon Gilmore but no negotiations have started, it was just a phonecall."
The parties are under intense pressure to strike a deal on a new coalition before the week is out and with the Dail (parliament) due to sit again on March 9.
Before any calls were made, all sides accepted a quick deal is needed as Ireland faces a series of challenging hurdles linked to its multibillion-euro bailout and banking crisis.
Mr Kenny is due to travel to Helsinki on Friday for a meeting of the European People's Party, with which Fine Gael is affiliated.
The contacts are intended to open the door for a charm offensive and garner support to renegotiate Ireland's 85 billion euro (£73 billion) loan from the International Monetary Fund (IMF) and Europe.
Mr Kenny has received a series of messages of congratulations from across Europe including German Chancellor Angela Merkel and European Commission president Jose Manuel Barroso.
Fine Gael said during all conversations with European leaders Mr Kenny raised the issue of the EU/IMF bailout.
Prime Minister David Cameron has invited him to Downing Street.
Mr Gilmore, who will meet left-leaning European colleagues separately this Friday, is in prime position to join a coalition after steering his party to second place.
But Fine Gael faces difficult talks with Labour with the sides at odds over the length of time it will take to turn around the budget deficit, tax, public sector cuts, water charges and how to tackle bondholder responsibility for banking debts.
Labour also warned it has its own parliamentary party hoops to jump through if it wishes to enter government.
Thrashing out a coalition with Independents could prove difficult given a sizeable amount of left-leaning TDs, while former stockbroker and Senator Shane Ross is also demanding a referendum on the IMF/EU loans.
Mr Kenny has vowed to force Europe's hand on renegotiation of the deal - but has made no mention of a referendum.
Fine Gael remains on course for about 75 Dail seats, just a handful shy of majority single party government in the 166-strong parliament.
His centre-right party continued to make gains on the second day of counting yesterday.
Meanwhile, their traditional rivals in Fianna Fail are reeling from high-profile losses across the country including outgoing Tanaiste Mary Coughlan, defeated in her Donegal South-West constituency and the loss of tourism minister Mary Hanafin's seat in Dun Laoghaire.
Finance Minister Brian Lenihan survived to become the only member of Fianna Fail to win a Dublin seat.
Mr Kenny and Mr Gilmore are expected to meet later today.
Roisin Shortall, Labour TD for Dublin North West, said she welcomed the first steps in attempts to strike a deal on coalition.
"My understanding is that the two party leaders are to meet later today, in the afternoon," she said.
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