Rising interest rates in the United States, the economic slowdown in China, the persistent fragility of the financial system in a number of countries and the effects of low oil prices on producer countries "all mean that global growth in 2016 will be disappointing and patchy," Lagarde wrote.
"And the medium-term outlook has clouded over, too, because low productivity, ageing populations and the fallout from the global financial crisis are putting the brakes on growth," she continued.
"The Fed is treading a tightrope: normalising interest rates, while at the same time seeking to avert any risk of disturbance on the financial markets," Lagarde said.
Generally speaking, outside the highly developed economies, "other countries are better prepared than in the past for higher interest rates," she wrote.
"Nevertheless, I'm worried about their ability to absorb shocks" that could be triggered by tighter monetary policy, Lagarde cautioned.
"A lot of countries have taken on more debt, much of which is denominated in US dollars," she argued.
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