Eurogroup President Jeroen Dijsselbloem said seven hours of talks in Brussels had been "constructive".
But they ended without a joint statement to outline procedural steps ahead of further talks next Monday.
Greece says its bailout deal with the EU is punitive and must end. The EU has warned Greece to abide by the deal.
The new Greek government was elected on a promise to end the bailout and ease the austerity measures that have accompanied it.
The government has proposed to overhaul 30% of its bailout obligations, replacing them with a 10-point plan of reforms.
However, Greece's creditors in the EU, led by Germany, have insisted that the terms of the bailout cannot be altered.
Officials from the two sides have been locked in negotiations aimed at reaching a deal on Greece's debt repayments that would stave off the prospect of its exit from the eurozone - a prospect viewed with fear by the markets.
Mr Dijsselbloem, who heads the Eurogroup eurozone finance ministers, said after the meeting on Wednesday that there had been no discussion of detailed proposals.
"We didn't enter into negotiations on content of the programme or a programme, we simply tried to work next steps over the next couple days," he said. "We were unable to do that."
"We had an intense discussion, constructive, covering a lot of ground, also making progress, but not enough progress yet to come to joint conclusions," he said.
Greece's finance minister Yanis Varoufakis struck an upbeat note, saying hours of emergency talks in Brussels had produced "very good discussions".
According to Reuters news agency, the Greeks had rejected a draft agreement from the eurozone finance ministers that proposed "extending" the current bailout deal.
The current EU-IMF bailout for Greece is due to expire on 28 February.
Greece's government, led by the radical left-wing Syriza party, says the conditions of the €240bn (£182bn; $272bn) bailout have impoverished Greece.
It rejects the "troika" team - the EU, International Monetary Fund (IMF) and European Central Bank (ECB) - overseeing the bailout's implementation.
The government, formed after Syriza won elections last month, is asking for a "bridge agreement" that will enable it to stay afloat until it can agree a new four-year reform plan with its EU creditors.
Greece's debt currently stands at more than €320bn (£237bn) - about 174% of its economic output (GDP).
On Wednesday, thousands of left-wing demonstrators rallied in Athens in support of their government's proposition.
The stakes of the talks over Greece's debt are high because of fears that a Greek default could push it out of the euro, triggering turmoil in the EU.
The Greek Defence Minister, Panos Kammenos, previously said Greece might seek funding from Russia, China or the US if it failed to reach a new debt agreement with the eurozone.
Source: BBC