MONTREAL--Reforms to the global financial system must go beyond the setting of capital and leverage ratios and include cultural overhaul at the world's leading banks, the head of the International Monetary Fund said on Monday.

Christine Lagarde said the financial world must understand that it is doesn't operate within a "bubble." She said the banking industry must learn "that it has to serve the economy, how it has to be successful by being sensible, and how it should focus on its mission."

Ms. Lagarde's remarks, made in Montreal at a blue-chip economics conference whose participants include former Obama administration adviser Larry Summers and ex-European Central Bank chief Jean-Claude Trichet, reinforce a message sent last month by Bank of England governor Mark Carney that the misdeeds of the financial sector threaten to undermine the public's support for free markets.

Also last month, Ms. Lagarde criticized the banking industry for delaying the implementation of reforms agreed upon after the financial crisis to prevent a similar shock from hitting the economy.

The global banking industry has been under a cloud following a wave of scandals at brokerage houses, including alleged rate-rigging of global benchmark rates, and because of how they dealt with mortgages during the financial crisis.

Ms. Lagarde's speech, which she made after being granted an honorary degree by the University of Montreal, also addressed the state of the global economy, which she said is turning a corner.

However, the recovery remains fragile, Ms. Lagarde said, and is at risk of stalling as a result of "complacency and fatigue" among policy makers.

In parts of the developed world, most notably Europe, there is the risk of what she described as "lowflation," or persistently meager increases in prices.

To combat the deflation threat, the European Central Bank last week cut its benchmark refinancing rate to a fresh historic low, 0.15%, and in an extraordinary move pushed the deposit rate, or what it pays banks to park funds overnight, into negative territory. The move is designed to push banks to lend, to stoke growth and, eventually, raise prices.

The ECB also said it would make hundreds of billions in cheap loans available to banks later this year, on the condition the banks increase their lending to the private sector.

"Clearly the recent stance by the ECB is welcome--whether it is the actual use of instruments or the use of words, it is coming at the right time. And we are encouraged to see they are willing to do more," she said.

The euro-zone recovery has come a long way, she added, but said more reform is necessary--including the promise to introduce a banking union. "All that is needed is for leaders to be courageous about it."

She also reiterated that she's not interested in the job as head of the European Commission, which she made known last week during a trip to London.