The European Union has failed to reach a deal on giving Greece more financial aid, prolonging uncertainty over the future of the debt-plagued country and the 17-member eurozone.
He said the finance ministers "made progress in identifying a consistent package of credible initiatives" aimed at making a further substantial reduction in Greek government debt.
There has been disagreement among the ministers and the International Monetary Fund, Greece's other bailout creditor, on how to make Athens' debt manageable. The eurozone ministers are in favour of giving Greece an extra two years, to 2022, to bring its debt to 120% of gross domestic product. The IMF has resisted such an extension.
Agreement on this issue is needed for the group of creditors to pay Greece the next batch of its rescue loans, expected to reach 44.6 billion euros (£35.7 billion). Greece needs the money to avoid bankruptcy.
Mr Juncker said he was optimistic that a deal could be reached. "We are very close to a result. We see no major stumbling block," he said. There are technical issues and calculations to be made in coming days, he said.
But IMF managing director Christine Lagarde sounded a more cautious note, saying only: "We have narrowed the positions."
Greece has been relying since 2010 on international bailout loans, under terms supervised by the so-called troika of the IMF, the European Central Bank, and the European Commission, which is the 27-country European Union's executive branch.
Greece reacted with dismay to the failure to release the funds, warning it is not just Greece's future that hangs in the balance. Prime minister Antonis Samaras stressed that Greece has done what its creditors from the EU and International Monetary Fund required.
"Our partners, along with the IMF, also must do what they have committed to doing," he said. He added that "it is not just the future of our country, but the stability of the entire eurozone" that depend on the success of negotiations in coming days.