Greek prime minister Alexis Tsipras has insisted that a deal to offer an economic lifeline to his debt-stricken country can be reached as leaders from the eurozone held crisis talks.
Mr Tsipras said he was ready for an "honest compromise" with the other 18 leaders in Brussels as they considered his application for a third bailout .
Greece has asked the European Stability Mechanism bailout fund for a 53.5 billion euro (£38.5 billion) three-year financial package, but many officials in Brussels say the figure will have to be much higher.
The country runs the risk of bankruptcy and crashing out of the single currency unless it can persuade the eurozone to agree the bailout in exchange for a package of economic reforms and further austerity measures
In a warning that the Greeks may not get the deal they need, German chancellor Angela Merkel, a key player in the negotiations, said there would "not be an agreement at all costs".
Mr Tsipras said: "I am here ready for an honest compromise. We owe that to the people of Europe, who want Europe united not divided.
"We can reach an agreement tonight if all parties want it."
The meeting of leaders from the eurozone nations follows protracted talks involving the single currency group's finance ministers.
Eurogroup president Jeroen Dijsselbloem, the Dutch finance minister, said: "We have come a long way, but a couple of big issues are still open, so we are going to put those to the leaders to decide."
All 28 European Union leaders, including David Cameron, had been expected to attend a meeting in Brussels, but now talks will be confined to politicians from the eurozone countries.
Business Secretary Sajid Javid said the UK economy was well prepared for the crisis if it remained confined to Greece - but said if the problem spreads across the eurozone, "who knows the impact?"
Asked if he thought Greece would be better off out of the single currency, he told BBC1's Andrew Marr Show: "That's going to be a decision for the eurozone countries, a decision for Greece and its partners. I have always thought the euro is a flawed proposal, right from the start, it was always going to lead to these kind of problems.
"I think it was entirely predictable and really the countries that are in the eurozone, they really have to draw lessons for all of them from this and realise that if they want a single currency they are going to have to have a single country to go with it."
He added: "The crisis, if it's confined to Greece – because you could say that this is probably the most well-telegraphed debt default in history, so British business, you could say, to some extent is prepared – so if it's confined to Greece I think we are well protected and there are likely to be very few problems, if any at all.
"If Greece exits the euro and it becomes contagious, then who knows the impact?"
Bank closures in Greece have been extended until Monday and Greeks are limited to withdrawing just 60 euro (£43) per day after the imposition of capital controls.
British tourists have been warned to take sufficient cash to cover expected costs and emergencies and to ensure they have supplies of their usual prescription medicines in case of shortages.