"The refugee crisis is a bit of a make or break, from my personal perspective," Lagarde said at the World Economic Forum (WEF) in the Swiss ski resort of Davos. Asked if it put in peril Schengen, she said: "Yes, I think so."
With more than one million migrants making their way to Europe last year and more still trying now despite the winter weather, the issue has been a key theme of the annual gathering of the rich and powerful in Davos.
French Prime Minister Manuel Valls warned Thursday that the EU was in danger of "fracturing" over several issues, including the migrant influx.
Some observers believe the huge inflows of migrants means Europe needs to tighten its borders.
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