In what she described as "a kind of open letter to my successor," Napolitano warned of terrorist threats, major weather events and the need to reinforce US border security.
"Our country will, for example, at some point, face a major cyber event that will have a serious effect on our lives, our economy, and the everyday functioning of our society," she said.
The administration has yet to name a successor for Napolitano, who resigned in July and will leave office next month after more than four years as the head of the Department of Homeland Security.
Napolitano warned of the "increasing likelihood of more weather-related events of a more severe nature as a result of climate change.
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"Napolitano's departure comes at a critical time, as Congress debates a major overhaul of the country's immigration system that would offer a path to citizenship for 11 million undocumented immigrants.
Possible replacements include New York police chief Ray Kelly, former US Coast Guard commandant Thad Allen and William Bratton, a former Los Angeles police chief, New York police commissioner and Boston police commissioner.