FRANKFURT—European Central Bank President Mario Draghi warned beleaguered euro-zone countries that there is no escape from tough austerity measures and that the Continent's traditional social contract is obsolete, as he waded into an increasingly divisive debate over how to tackle the region's fiscal and economic troubles.

In a wide-ranging interview with The Wall Street Journal at his downtown office here, Mr. Draghi reflected on how the region's travails were pushing Europe toward a closer union. He said Europe's vaunted social model—which places a premium on job security and generous safety nets—is "already gone," citing high youth unemployment; in Spain, it tops 50%. He urged overhauls to boost job creation for young people.

There are no quick fixes to Europe's problems, he said, adding that expectations that cash-rich China will ride to the rescue were unrealistic. He argued instead that continuing economic shocks would force countries into structural changes in labor markets and other aspects of the economy, to return to long-term prosperity.

"You know there was a time when [economist] Rudi Dornbusch used to say that the Europeans are so rich they can afford to pay everybody for not working. That's gone," Mr. Draghi said.

"There is no feasible trade-off" between economic overhauls and fiscal belt-tightening, Mr. Draghi said in the interview, his first since Greece sealed its second bailout.