Three of the dead were found outside the train, and one was found inside, authorities said. Their families haven't yet been notified.
Eleven people are believed to be in critical condition, authorities said. The train operator was among the dozens injured, Cuomo said.
Metropolitan Transportation Authority spokeswoman Marjorie Anders said the big curve where the derailment occurred is in a slow speed area. The black box should be able to tell how fast the train was traveling, Anders said.