German chancellor Angela Merkel has said all 19 eurozone members believe the bailout deal agreed today with Greece can work.
Taoiseach Enda Kenny admitted the negotiations were difficult.
"This has been a pretty bruising experience," he said, "but (it) allows for a document that will be the basis for negotiation for a third programme for Greece, which will allow the Greek economy to thrive and prosper and continue to remain a member of the Eurozone."
The Greek government had requested a three-year, €53.5bn rescue package from Europe's bailout fund.
In return for a commitment from Greek Prime Minister Alexis Tsipras to push through pension, market and privatisation reforms, the 18 other eurozone leaders agreed to start talks on a new bailout.
The deal means that the European Central Bank can continue to support Greece’s beleaguered banks, which have come close to collapse.
Tánaiste Joan Burton said that the outcome of the European talks indicates that Sinn Féin and other left-wing parties wouldn't be able to deliver on election promises.
"Sinn Féin's version of economics on default is seriously lacking in any realistic understanding of the incredible hardship that that would impose on the people of any country where there was a default,” she said.
"I would suspect that that's sloganeering, rather than actually talking about economics and talking about prosperity and jobs and business for people in a country."
Commenting on the outcome of the EU summit meeting this morning, Sinn Féin President Gerry Adams said: “The conduct of a number of EU governments over the past number of weeks has been alarming.
“They have effectively closed down the Greek banking system and held the Greek Government and people to ransom.
“To its shame the Irish Government took the side of the strong against those in need of support and solidarity.
“It is obscene for Fine Gael, Labour and Fianna Fáil to lecture the Greek people while generations of Irish people will be paying off debts that are not of their making.
“The decision is now with the Greek government and parliament. I wish them well in their deliberations.
“Today could well be the day when all pretence of a Europe of equal states and people was lost and replaced by a Europe of the powerful and the wealthy.”