Ministers did not agree on releasing new loans to Athens, but Dijsselbloem said work is progressing towards a next disbursement "before the summer".
He added: "With EU creditors now expected to finally sign off on Greece's latest injection of rescue cash, the European Commission expects growth to bounce back to 2.6 per cent this year".
Euro-area finance ministers committed last May to a set of potential measures to ease the repayment terms on Greek bailout loans after the end of the program in 2018, but the degree to which these measures will be implemented is still a subject of contention.
Greece's debt mountain stands at a towering 180 percent of annual output, the legacy of a crisis that brought panic to the markets and almost forced the country out of the euro.
Germany is thought to be the country most adamantly against debt relief measures, with its finance minister Wolfgang Schaeuble claiming Greece would have to leave the eurozone before debts are written off.
"This afternoon and this evening we had a first in-depth discussion on the topic of debt sustainability, looking very carefully at needs, options, constraints", Dijsselbloem said. "Yes, this agreement is possible, is doable, is near and we should make all our best efforts to get there", Moscovici told reporters before the meeting.
Athens needs funds to repay 7.5 billion euros (6.4 billion pounds) of debt maturing in July.
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.
The discussions in Brussels lasted for some seven hours.
"It's time for the International Monetary Fund to come aboard", he added.
The other participants in the meeting were left waiting in the room to hear if any progress had been made.
Neither Greece's global creditors, nor the German government, one of the main sponsors of the bailout, have reached an internal consensus on how to ease the heavily-indebted nation's debt burden without impairing its growth and development prospects.
Greece has also demanded more debt relief and, having passed new austerity measures in May, believes it has done more than enough to earn it.
"It was a hard discussion", Greek finance minister Euclid Tsakalotos said after Monday's meeting.
He regretted that the creditors had failed to give "clarity to the Greek economy and the financial markets". The next gathering is scheduled for June 15 in Luxembourg.
Mr Macron's office said the president spoke to Greek prime minister Alexis Tsipras and stressed "his determination to find an accord soon to lighten the burden of Greek debt over the long term".
Greek and European Union officials said that a proposed final compromise was considered too vague by the Athens delegation, which rejected the draft plan arguing it wouldn't bring sufficient certainty on the country's debt prospects.
One potential ally for Greece is Emmanuel Macron, France's new president.