Greek finance minister Yanis Varoufakis has conceded that time is pressing for the country to secure a deal, but believes an agreement that is acceptable for all can still be reached.
Greece is in talks about what reforms it must make to get more loans. It needs outside financial help if it is to meet debt repayments as soon as June 30.
After a eurozone meeting failed to reach a deal, Mr Varoufakis said the Greek government accepts that the country needs fundamental reforms.
He said, however, that those pursued in recent years have led to huge hardship, including high debt, unemployment, poverty and emigration.
"There is no question that Greece needs to make adjustments," he said. "The question for us is: What kind of adjustments?"
Earlier Eurogroup president Jeroen Dijsselbloem said Mr Varoufakis presented too few measures that were credible and serious at a meeting today.
The talks over the last week have not progressed and "time is running out", Mr Dijsselbloem said.
He added it is up to the Greeks to submit new proposals in the coming days.
Greece is in talks to get more loans from its creditors - which include the eurozone states and the International Monetary Fund (IMF).
Without help, Greece will struggle to make a debt repayment on June 30.
Valdis Dombrovskis, an EU vice-president whose remit includes the euro, wrote on his official Twitter account that there was no deal at the meeting of the eurozone's 19 finance ministers in Luxembourg.
He added that there was a strong signal for Greece "to engage seriously in negotiations".
Mr Dombrovskis added that the group of eurozone finance ministers "stands ready to reconvene at any moment".