All EU countries now need to prepare to give humanitarian aid to Greece, said German Economy Minister Sigmar Gabriel at a press conference. "We cannot leave Greece alone," he added.
Gabriel said Greece must present a new offer that goes beyond its previous proposals if it wants to remain in the euro, adding that Athens soon faced state insolvency.
"If Greece wants to stay in the euro, the Greek government must quickly make a substantive offer that goes beyond its willingness thus far," he told a news conference.
Earlier on 6 July, European Commission vice-president Valdis Dombrovskis said: "The place of Greece is and remains in Europe.
"The crisis in Greece does not threaten the financial stability of the entire eurozone. We have all the necessary instruments to ensure it, including the stabilisation fund of €500bn."
Dombrovskis said the no vote has made life much more "difficult" for the Greek government but the ball is in their court to now come up with some credible reforms.
He also said the question at the referendum in Greece was "neither legally nor factually correct" since the second financial aid programme by the creditors had expired on 30 June.
The EU has given Greece more than €184bn in macro-financial assistance over five years through its stabilisation mechanisms, the European Financial Stability Facility (EFSF) and Greek Loan Facility (GLM) noted the EC's vice president.
The two bailout packages for Greece since 2010 are estimated at €240bn.
Over 61% of Greek voters said no to the conditions of the country's creditors, the EC, European Central Bank and International Monetary Fund.
The referendum followed a week that saw Greece's banks closed and capital controls imposed, as the country teeters on the edge of complete financial meltdown.
Prior to the Dombrovski's press conference, a spokesman for the German government said it is still focused on keeping Greece inside the single currency and the country must now make the first move.
Germany, which is the largest holder of Greek debt, said it would not accept a cut in the country's debt.