But Germany's Wolfgang Schaeuble is sticking to his insistence that further-reaching debt relief is a matter for the future.
Other eurozone finance ministers arriving for the meeting in Brussels soon followed suit, with Belgium's Johan Van Overtveldt cautioning "we should ... consider all the consequences of an eventual debt relief".
The executive Commission, which is one of the overseers of Greece's bailout, sought to downplay fears that Greece was heading for another financial crisis.
Eurozone finance ministers failed to reach an agreement for fresh bailout funds for Greece after a meeting in Brussels, said Eurogroup President Jeroen Dijsselbloem on Monday.
Greece is locked in negotiations with creditors in an effort to release another tranche of bailout funds to repay debts that fall due in July, as a second review into its progress has dragged on for months.
However, ministers concluded that Athens still had to take some further measures.
He said 3.5 percent of gross domestic product was a high primary surplus target which, however, "we were forced to accept".
"We've not reached an overall agreement on that part of the discussion".
"It should not be beyond the wit of man to find an agreement", Greek Finance Minister Euclid Tsakalotos said after the crunch talks.
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The issue at hand: whether a lower court acted properly in issuing a nationwide injunction to keep the order from being enforced. A 2015 Supreme Court opinion written by Justice Kennedy has become a pivotal precedent in the legal fight.
However, he also said he was optimistic that a definitive deal could be brokered by the time of the next formal meeting in June.
After the Eurogroup meeting, French finance minister Le Maire said that Germany's role had been "constructive" but that he "would be lying if [he] said that France and Germany have no difference over the sustainability of Greek debt".
Dijsselbloem said he expected a deal to be struck between Greece and its creditors at the next Eurogroup meeting in June.
The sticking point is the International Monetary Fund joining the loan programme amid some debt relief for Greece.
"Here we are making progress, there are not doubts about that, but we are not quite there yet", he said.
Without the loans, Athens is likely to default - a bad start for a country that wants to return to market financing next year when its latest bailout, the third since 2010, ends in mid-2018.
Euro zone officials say a report prepared by experts on whether Greece has implemented what is called "prior actions" - laws that have to be passed to make the reforms stick - is positive.
The IMF has more conservative estimates about both these outcomes than Greece's euro-area creditors, in turn suggesting the country needs greater debt relief.
Schaeuble, as well as several International Monetary Fund economists, agree that Greece should demonstrate its ability to decrease its budget deficit and achieve sustainable economic growth by the early 2020s through an economic reform package that would include stricter austerity, improved investment climate, deregulation, and abandonment of the most costly social programmes.