Ministers next meet on 15 June, but Greece needs the new funding in order to make a €7.3m (£6.3bn) loan repayment due in July. But that was the easy part of their discussions.
He said the ministers needed to consider "additional options or adjusting our expectations".
"We have made huge progress on the policy package on which so much work had been done in the last months and on which an agreement had been reached between Greece and the institutions", Dijsselbloem said.
"I'm sure the efforts we put in are not going to be in vain".
Greece's finance minister, Euclid Tsakalotos, said: "Greece has done its bit, most would say more than its bit".
While austerity measures over the past seven years have seen Greece's annual budget position improve markedly, the country's debt burden stands at around 180 percent, a level that the Greek government and the International Monetary Fund think is unsustainable in the long-term - hence the insistence on some debt relief.More news: Matching Senna's poles would be unreal for Hamilton
Germany has led a coalition of euro zone countries pushing for International Monetary Fund involvement to balance what some argue is an overly lenient approach from the European Commission.
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.
But Germany is wary because doing any favours for Athens is deemed a vote killer ahead of general elections in September.
Greece is now in the midst of its third bailout program - the current three-year program expires in the summer of 2018 and could be worth up to 86 billion euros ($95 billion) in total.
Monday's talks came four days after Greece's Parliament passed a major austerity bill created to save $4.5 billion in the next three years through pension cuts and tax increases.
The German Foreign Ministry sees the Greek bailout as primarily a political tool that would allow for a greater consolidation of the Eurozone and strengthening Germany's leadership in the bloc, both economically and politically.More news: United Kingdom police make 7th arrest in Manchester terror probe
He said the finalization of an agreement on Greece would have to wait for a report on whether the country has implemented all the agreed reforms, the so-called compliance report, which euro zone officials said was positive.
Referring to Britain's looming exit from the EU, Le Maire stressed France and Germany meant to seize any opportunities for their financial industries. "I'm quite confident that if all sides are in a mood to compromise, it should not be beyond the wit of man to find that compromise within three weeks", he said.
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.
Sigmar Gabriel, Germany's Social Democrat vice chancellor, told the daily newspaper Sueddeutsche Zeitung Monday that Germany should agree to a bailout deal.
Greece's debt stands at almost 180 percent of annual output, the legacy of a crisis that brought panic to the markets and almost forced the country out of the eurozone.More news: Andy Burnham: Manchester mayor's statement in full