Germany's fiscal hawks faced off against doves led by France at a summit of the 19 eurozone leaders in Brussels, with Athens facing demands to push through new reform laws next week.
Despite the fact Greece's banks could run dry soon, an emergency summit of all 28 EU leaders billed as the last chance to keep the country in the euro was called off due to slow progress.
Greece's leftist Prime Minister Alexis Tsipras insisted a deal was possible tonight "if all parties want it", adding that he was ready for an "honest compromise".
"There will be no agreement at any price," Merkel told reporters, complaining of a loss of trust in Athens and warning of "tough negotiations" ahead.
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French President Francois Hollande, whose country has been the most supportive of Athens during the six-month standoff, meanwhile said Paris would do "everything" to keep Greece in the euro.
In a sign of the growing tensions between the eurozone's two biggest economies and political forces, Hollande also ruled out a German proposal for a "temporary Grexit" from the single currency.
They agreed Greece would have to push through new laws by Wednesday under the conditions agreed by the eurozone ministers, Finnish Finance Minister Alex Stubb said afterwards.
Athens would also have to introduce tough conditions on labour reform and pensions, VAT and taxes, and measures on privatisation, he said.
"We have come a long way but a couple of big issues are still open," Eurogroup chief Jeroen Dijsselbloem said. "We are going to put those to the leaders so it's up to them."
Tension turned to anger last month after Tsipras called a referendum on the bailout terms, in which Greeks overwhelmingly rejected the creditors' demands.