The ECB has taken some of the heat out of the euro zone debt crisis by last month unveiling its new bond-purchase program - dubbed "Outright Monetary Transactions", or OMT - but Draghi urged governments not to become complacent with reforms.
"Within the European Monetary Union, progress needs to be made in three areas: budgetary policy, structural reforms and financial market regulation," he said in the text of a speech for delivery via video link to Venice's Ca' Foscari University.
Calling for greater economic integration among euro zone states, Draghi said no country in such a currency union should be allowed to cause economic damage to other members by pursuing its own national economic policy priorities.
His message came as the ECB, the European Commission, and the International Monetary Fund - the so-called troika of international lenders - work on a review of their 130 billion euro bailout program for Greece.
Draghi said it was vital there be multilateral surveillance of budget policies in the euro zone. He called for structural reforms to promote innovation and for centralized authorities to be created to limit excessive risk taking in financial markets.
He said the European Commission's recent proposal for a single banking supervision mechanism for the euro area - in which the ECB would play an important role - was "a bold and necessary step towards creating a single financial market which ensures financial stability in the euro area and the European Union."
(Writing by Paul Carrel; editing by Jason Webb)
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