The eurozone-IMF standoff has held up a tranche of bailout funds that will let Greece repay 7.0 billion euros of loans due in July.
Pierre Moscovici said before the eurogroup meeting that a deal is "doable" and that it's time to "open a new phase, a new page" with regard to Greece.
Greek lawmakers approved a series of tax rises and pension cuts last week, over and above the previous dozen cuts to its national pensions since the onset of the crisis in 2010 and the crippling austerity.
Greece's debt mountain stands at a towering 180 percent of annual output, and the country is now back in a recession despite emerging from its economic depression in 2014.
The fund is refusing to take part in the rescue unless some of Greece's hefty debts are written off.More news: Jose Mourinho sends message to Man United fans about summer transfers
He said that the IMF was ready to join the programme, a condition for new disbursements to Greece set by some countries such as Germany, but the fund needed more clarity on what the euro zone can offer in terms of debt relief before making a final decision. He, like Dijsselbloem, said that "extra measures if required" would come after the bailout program expires next year.
The French economy minister said that the discussion of the Greek debt at the latest meeting was constructive and that it was "perfectly normal" that an agreement had not been reached since the issue at hand was very complex.
Tuesday's deal included the approval of the next batch of bailout money, but also an agreement on the sort of debt relief measures Greece can expect to get when its current bailout programme ends next year.
After more than eight hours of talks in Brussels, ministers from the 19-member single currency bloc could not settle deep differences on debt relief pitting Germany, the eurozone's most powerful member, against the International Monetary Fund.More news: Marking difference with US, France urges dialogue with Iran
But some European countries, including Germany, say any debt relief should be considered in 2018, anxious that concessions could affect the pace of economic reforms in Athens.
Greece's European Union creditors have once again failed to reach an accord over the amount of debt relief the Hellenic state should get, once the country's €86 billion bailout program ends in mid-2018.
Additional debt relief is also necessary for the European Central Bank to include Greek bonds in its asset purchases program, which would ease the country's access to bond markets. Bruno Le Maire and Wolfgang Schäuble flew to Brussels in the same plane, after a press conference in Berlin where they announced a working group on eurozone reform.
"I really mean it, and if not, then it will be in the coming weeks", he said.
Successive Greek governments have slashed spending in return for bailout money to avoid bankruptcy.More news: Day 100: Lawmakers draft tax filled budget fix; may debate school funding
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