Deutsche Bank and many other major banks need to reexamine their business models to maintain long-term profitability in a very low interest rate environment, International Monetary Fund Managing Director Christine Lagarde said on Thursday.

Lagarde told Bloomberg Television at the IMF and World Bank fall meetings in Washington that Deutsche Bank must "decide what size it wants to have and how it wants to strengthen its balance sheet. But it's not the only one in the banking basket that has to do that job."

During an earlier news conference, Lagarde said many banks around the world need to revamp their business models to deal with current ultra-low rate financing conditions, and that the IMF believes there are the means and a determination to do so.

Market worries about Deutsche Bank's balance sheet in the face of a U.S. government demand for $14 billion in fines have cast a shadow over the start of the IMF and World Bank meetings, which will include the world's top finance leaders and commercial bankers.

Lagarde told Bloomberg Television that a settlement of U.S. Department of Justice charges over Deutsche Bank's sales of mortgage-backed securities leading up to the 2007-2009 financial crisis would be welcome because it would provide some certainty over the impact on the bank's balance sheet.

Regarding Germany's proposed, 6-billion euro tax cut plan , Lagarde said she hoped it would be part of a larger fiscal spending plan that "will exploit the fiscal space that Germany has available" and include infrastructure investments.

"Given the very, very low financing costs, particularly for a country like Germany, it is certainly the right time to develop infrastructure further," Lagarde said in the news conference. "It's not just about Germany, let's face it. Every country can do something."