Gurria's comments come as all eyes focus on the Greek poll this weekend, when citizens will vote either "yes" to more austerity – and effectively a future in the euro zone -- or "no," and a potential exit from the single currency.
The latest opinion poll, conducted by the ALCO polling institute and published in the Ethnos newspaper on Friday, pointed to a close result. The "yes" vote supporting creditors' reform proposals came in at 44.8 percent, the "no" vote stood at 43.4 percent, and 1.8 percent were undecided.
However, it also showed that 74 percent wanted to remain in the euro, against 15 percent, who wanted a "national currency."
Gurria warned that it was in everybody's interest "to keep Europe together" although he said he recognized that there were political, legal and financial constraints on the bodies which oversee Greece's bailout -- the International Monetary Fund (IMF), European Central Bank (ECB) and European Commission.
"The solution will come from the understandings of those constraints, and at the same time -- and I think this is actually going to happen -- of moving above the shorter-term interest in the understanding that it's in everybody's interest to keep Europe together," he added.
Although talks between the radical left government in Greece and its lenders have been ongoing since February, Greece's crisis peaked last Friday night when Prime Minister Alexis Tsipras announced a referendum.
Poll: How should the Greeks vote?
That move prompted the ECB to cap its emergency funding for Greek banks and capital controls have been imposed, which are expected to remain in place until after the vote. Now banks' cash reserves are reportedly running out, with the daily allowance from ATMs reduced from 60 euros to 50 euros.
The ECB's policymakers are expected to next discuss further emergency funding assistance (ELA) for Greek banks on Monday, a person familiar with the matter told Reuters Thursday.