Taoiseach Enda Kenny has said he is hopeful that a resolution to the Greek funding crisis can be reached this weekend.

He said there was unanimity among those present at the summit in Brussels last night that Greece should remain within the euro zone.

“Obviously there are discussions going on today and tomorrow and hopefully a conclusion can be reached this weekend,” Mr Kenny said.

He said the Greek prime minister had been open about targets and objective which had been set.

“Obviously these things have to be financially sustainable and they have to make economic sense and they have to be fair,” Mr Kenny said, prior to the Cabinet meeting this morning.

“I think that around the table yesterday evening there was absolute unanimity there should be no exit by Greece from the euro zone.

“And that everybody would work together with the institutions and the government in Greece to work this out so I hope that can happen.”

Shares have risen after Greece’s latest budget proposals raised hopes it would stave off a debt default and reach a deal with lenders later this week.

Greece has been granted a two-day reprieve in its campaign for new rescue loans as it comes under extraordinary pressure from euro zone leaders and the European Central Bank to comply with their conditions for aid.

Across Europe the markets reacted well to the prospects of a Greek deal with the blue-chip Euro STOXX 50, up 0.8 per cent. The FTSE 100 Index added 0.3 per cent to 6,846.87 in early trading while the ISEQ Index added 0.4 per cent.

Athens submitted the revised funding proposals to its international creditors, but a day of emergency talks in Brussels yielded no new funding arrangement.

After weeks of stalemate, finance ministers directed euro zone officials to enter fresh talks with Greece, in anticipation of a deal before EU leaders return to Brussels on Thursday for their second summit of the week.

German chancellor Angela Merkel said time was running very short but she hoped the next summit would have nothing more to do but take note of an agreement with the ministers. While it was clear that financial sustainability would have to be discussed, she noted that Greece did not have big debt repayments for many years.

European Commission chief Jean Claude Juncker said: "I simply wanted to say that the proposals that the Greek government was submitting to our mediation tonight and early this morning – although these proposals were coming in with some delay – are a major step taken by the Greek authorities."

China said it hopes Greece gets out of its debt crisis at an early date. Foreign Ministry spokesman Lu Kang said that China has noted the close communication among the relevant parties surrounding the debt crisis in Greece.

“From China’s standpoint, we hope Greece will get out of the crisis soon so as to enable the stable development of the EU integration process,” Lu told a daily news briefing.

With Greek banks under mounting strain due to large deposit withdrawals, the ECB is increasing emergency aid to the lenders on a day-to-day basis only.

The Financial Times reported Minister for Finance Michael Noonan – together with German minister Wolfgang Schäuble – pressed at a meeting of euro zone ministers for curbs on emergency support for Greek banks unless capital controls were imposed.

Mr Noonan’s spokesman declined to comment on the ministers’ discussion on the basis that such meetings are private.

When it was put to him that international media were reporting that Ireland wanted capital controls in Greece, the Minister’s spokesman said: “The issue for Ireland is to ensure we have clarity around the proposals and the process. Our objective is to ensure that Greece negotiates a satisfactory conclusion and remains in the euro zone.”

It is understood that Mr Noonan raised the increasing reliance of the Greece banks on emergency liquidity assistance from the ECB with fellow ministers. He is understood to have asked how long Greece could continue in a situation in which the ECB was meeting daily to decide how much money it was putting into its commercial banks. He also asked how much time was available for a political solution to settle that matter.

In light of this intervention, and that of Mr Schäuble, ECB president Mario Draghi said his institution's support for Greek banks was not an issue for ministers to decide. The ECB governors would continue to review the situation on a daily basis, he said.

Additional reporting: Reuters