Joel Zaritsky, a passenger on the train, injured his hand in the crash and was on his way to New York for a dental convention, according to the Associated Press.
"I was asleep and I woke up when the car started rolling several times. Then I saw the gravel coming at me, and I heard people screaming. There was smoke everywhere and debris. People were thrown to the other side of the train," Zaritsky told the Associated Press.
President Barack Obama says his thoughts and prayers are with the friends and families of the victims of the fatal train derailment in New York City.
The White House issued a statement saying the president was briefed on the accident Sunday morning.
The White House says Obama will continue to stay in touch with New York officials throughout the day.
At least two of the cars had flipped on their side after the crash, and one car stopped only feet from the banks of the Harlem River. Cuomo told reporters that the four fatalities were from the two cars that had flipped on their side.
Frank Tatulli, a passenger on the first car to derail, told WABC-TV he had managed to get off the train by himself after the derailment but other passengers had to be removed by stretchers. Tatulli, who said he takes the train every Sunday, said he felt the train was traveling at a faster than normal speed.
"Four people lost their lives today in the holiday season," said Cuomo, who said the families had not been notified. "Let us all say a prayer and remember those people we lost this morning."
A senior State Department official told ABC News there was no indication that the crash was a result of terrorism or criminal conduct.
Metro-North announced that rail service was indefinitely suspended between the Tarrytown and Grand Central stations in New York. Amtrak Empire service was halted for hours between New York City and Albany but resumed Sunday afternoon, with some delays.
The Associated Press contributed to this report.