Eurozone leaders have talked through the night in Brussels in a bid to agree terms for a new bailout for Greece.
Reports say a draft compromise has been put to the emergency summit but no details have emerged so far.
Without a new bailout, Greece's banks face collapse and the country could exit the euro.
Greece is being told to pass legislation on a series of reforms by Wednesday before any talks on another bailout can begin.
But the BBC's Chris Morris in Brussels says there is still no agreement on exactly what Greece has to do.
Earlier, eurozone finance ministers submitted a list of measures to the leaders following two days of fraught discussions.
But one Greek government official called the proposals "very bad". Another said some of the proposals appeared designed to "humiliate" Greek Prime Minister Alexis Tsipras and his left-wing Syriza government.
The summit was paused for several hours overnight to allow talks between Mr Tsipras, German Chancellor Angela Merkel, French President Francois Hollande and European Council President Donald Tusk.
Early on Monday, Mr Tusk's spokesman announced the summit was reconvening to discuss a "compromise proposal".
The four-page document of draft proposals put forward by eurozone finance ministers include:
- Reforms set out by Greece to be ratified by parliament by Wednesday, 15 July
- "Ambitious" reforms to pensions and labour markets
- International creditors to work on the ground in Athens and have full oversight of draft legislation
- Possible transfer of €50bn in "valuable" Greek assets to external fund for eventual privatisation
- Possible talks on "swift negotiations on a time-out from the euro area, with possible debt restructuring" if a bailout is not agreed
However, one senior EU official said there was no chance of "time-out" proposal surviving in any final document to be approved by eurozone leaders. Another official said there was no provision and therefore no legal basis for such an arrangement in the EU treaties.
Reports also emerged that Greece was holding out over the proposed role of the IMF in the new programme and over the independent fund to hold Greek assets.
Tough choices for Greece - by Paul Kirby, BBC News website Europe editor
There may only be four pages, but if this draft document is agreed, it would be an extremely difficult pill for Greeks to swallow.
For Alexis Tsipras and his left-wing Syriza-led administration, some of the ideas would be little short of humiliation.
Even if Greek MPs pass sweeping reforms by Wednesday, the government would have to allow international creditors full monitoring of its work in Athens and agreement of draft laws in advance.
Syriza came to power promising an end to such oversight.
Another possible step is to "amend or compensate" for any laws Syriza pushed through that ran counter to what was agreed with the eurozone in February.
That might mean overturning the reinstatement of 4,000 civil servants such as school guards and cleaning ladies.
Arriving for Sunday's meeting, Mr Hollande dismissed any suggestion of a "time-out" for Greece.
"There is no temporary Grexit, there is a Grexit or there is not a Grexit," he said, adding that he would "do everything to find a deal tonight".
Mr Tsipras was also upbeat, telling reporters: "I'm here ready for an honest compromise... we can reach an agreement tonight if all parties want it."
But Mrs Merkel said "the most important currency has been lost... trust and reliability" in the last few months of negotiations with Greece, and there would be "no agreement at any price".
"We have to make sure the pros outweigh the cons - for Greece's future, for the entire eurozone and the principles of our collaboration," she said.
The head of the European Parliament, Martin Schulz, said a deal was absolutely vital to the future of Europe.
"The alternative will be that over the next few years we are going to find ourselves in a catastrophic state of affairs as far as Greece is concerned," he told a news conference in Brussels.
Greece in numbers
Greece's debt mountain
177% country's debt-to-GDP ratio
25% fall in GDP since 2010
26% Greek unemployment rate
The Greek government earlier this week set out a new list of austerity measures to try to secure the bailout.
They included many measures that had been rejected by the Greek people in a referendum a week ago.
Despite this the proposals won the overwhelming backing of Greece's parliament in the early hours of Saturday morning.
Technical experts from Greece's creditors - the European Commission, the European Central Bank and the International Monetary Fund - also said the proposals were a basis for negotiations.
However, as eurozone finance ministers gathered on Saturday in Brussels it became clear that countries were divided over the issue of a third bailout for Greece.
Reports have emerged of a "tough, even violent" atmosphere at times as the talks went on into the night.
Germany's Wolfgang Schaeuble, who has taken a tough line on Greece, seemed to be at the centre of much of the heated debate, Reuters news agency reports.
One participant said Mr Schaeuble had to speak with French finance chief Michel Sapin to clear the air before the talks resumed on Sunday.
One who was noticeably keeping a calm head was said to be Greece's new finance minister Euclid Tsakalotos.
But time is running out to prevent Greece's economic collapse.
Banks have been closed for two weeks and a €60 daily limit on cash machine withdrawals, imposed on 28 June, remains in force for Greek citizens.
There is little money left in the banks and public sector workers are due to be paid this week.
Greece fell into arrears on an IMF repayment on 20 June and faces a €3bn payment to the European Central Bank on 20 July.
It has already received two bailouts totalling €240bn since 2010.
Economy Minister Giorgos Stathakis told the BBC on Saturday that if there was a new deal, banks could reopen within the week, but he admitted it could take a "few months" to remove capital controls.