Taoiseach Enda Kenny has written to the Greek Prime Minister tonight asking him to return to the negotiations to find a solution to the country's economic crisis.
Mr Kenny was responding to a letter from Alexis Tsipras in which the Greek prime minister sought support for an extension of its bailout programme for one month.
Mr Tsipras is seeking support from European leaders for an extension to the bailout programme.
In a letter to Mr Kenny, he said the Greek parliament had agreed to a referendum on proposals to settle the crisis.
In order, he said, to carry out the poll in a calm and positive climate without external pressure, an extension of the bailout programme should be supported.
He said negotiations would then resume next Monday on reaching an agreement based on the result.
He asked the Irish Government and other EU governments to re-examine their position.
In a response tonight, the Taoiseach said he had hoped that agreement would have been reached at the Eurogroup meeting on Saturday.
He added that the Greek government's decision to break off from the negotiations had meant that this was not possible at that time.
Mr Kenny said he hoped it would be possible to return to negotiations as quickly as possible.
He added that Ireland had experienced a very difficult economic period and worked its way through a programme of assistance and had great empathy for Greece and its people.
He added that the door remains open to dialogue.
Meanwhile, the Economic Management Council met in Dublin this evening to discuss developments in Greece and across the eurozone.
During the meeting it received briefings from Central Bank Governor Patrick Honohan and National Treasury Management Agency officials.
The meeting took note of the calm in the Irish financial markets.
The Government intends to keep developments in Greece under review.
Harris says lack of engagement 'cannot continue'
Minister of State at the Department of Finance Simon Harris has encouraged the Greek government to come back to the negotiating table, describing the situation as highly regrettable.
Speaking on RTÉ's Six One News, Mr Harris said that if Greece leaves the euro, it will be disappointing and a bad day for Europe.
He said it is encouraging to see that there has been little movement on the bond markets.
However, he said, a solution is needed, adding that the lack of engagement from Greece cannot continue.
Progress had been made, he said, but that, almost out of the blue, Greek negotiators unilaterally withdrew.
Mr Harris said: "We certainly haven't given up hope and I don't think any of the 18 Eurogroup colleagues have.
"If Greece leaves the euro, it will be a very disappointing day and a bad day for the euro."