Earlier talks between Greece and its eurozone creditors broke down without agreement on a way forward as the country seeks to ditch its bailout deal.
But Prime Minister Alexis Tsipras, whose hard-left Syriza party took office in January, has since been more optimistic.
The talks have been continuing to explore the possibility negotiating new terms before Monday.
The bailout talks are the latest stage in a long-running crisis over Greece’s huge debts, run up during years of overspending including the 2004 Athens Olympics.
Mr Tsipras has now revealed his austerity-light replacement plan for the bailout, which he is optimistic will convince EU member states to agree a new deal.
“I am very confident that all together we can find a mutually viable solution, in order to heal the wounds of austerity and to tackle the humanitarian crisis across the European Union,” he said as he arrived for the talks.
But he warned the negotiations posed a “crucial turning point for Europe”.
Failure to agree a deal could mean Athens might default on its debt, in which case it would almost certainly crash out of the 19-country eurozone.
Speaking outside the talks David Cameron said the stalemate needed to be resolved.
“What is required between Greece and the eurozone is not a stand-off but a solution,” he said.
“The British economy is growing and succeeding but we are affected by the situation on the European continent and the longer that the stand-off goes on, the worse that could potentially be for Britain.
“That underlines the importance of sticking to our long-term plan.”
Athens has promised a 10-point plan which will include renewed efforts to tackle tax evasion and corruption but also promote employment.
One condition of its EU-International Monetary Fund rescue was delivering a primary budget surplus of 3% in 2015 before debt repayments.
The new government has argued such targets – achieved through tax hikes and wage cuts – make an economic recovery impossible and it is pushing to halve that figure to 1.5%, a result it delivered in 2014.