But German Chancellor Angela Merkel took a tough line as usual, echoing her usual position and that of several mainly newer eastern European euro members.
"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.
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.
The meeting came after the Eurogroup of eurozone finance ministers finished two days of intense talks on Greece's proposals for reforms in exchange for a three-year bailout worth 80 billion euros (NZ$132.57 billion).
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."
Greece and its creditors have been at odds since Tsipras was elected in January on a vow to end five years of bitter austerity under two bailouts since 2010 worth 240 billion euros.
Tension turned to anger last month after Tsipras called a referendum on the bailout terms, in which Greeks overwhelmingly rejected the creditors' demands.
Greece's parliament approved fresh proposals by the government in Athens in the early hours of Saturday, despite the fact they were largely similar to many of those rejected in the referendum.
In Greece, there is growing alarm at capital controls that have closed banks and rationed cash at ATMs for nearly two weeks, leading to fears that food and medicine will soon run short.
The European Central Bank is providing emergency liquidity to keep Greek banks afloat but has frozen the limit, with fears that failure to reach a deal could cause it to shut off the taps completely.
- AAP
