Cuomo told CBS This Morning that the note was found by investigators probing the attack.
Eight people were killed and at least 11 seriously injured after a rented pickup truck was driven onto a bike path near the World Trade Center.
The suspect, identified by authorities to the Associated Press as Sayfullo Saipov, an immigrant from Uzbekistan who was living in New Jersey at the time of the attack.
The attacker rented the pickup around 2 p.m. Tuesday then drove into the city and rammed people on the bike path an hour later, authorities say. He drove on the path for about 14 blocks before slamming into a school bus.
"A person hopped out of the car with two guns and started yelling and screaming," said a 12-year-old student at a nearby school told the Associated Press. "They were yelling 'Allahu Akbar.'"
He was shot by an officer on patrol in the area and taken to a nearby hospital in critical condition.
New York City Police Commissioner credited his officer for stopping the "carnage soon after it began" with the use of force during a Tuesday press conference.
Mayor Bill de Blasio called the attack "an act of terror, and a particularly cowardly act of terror aimed at innocent civilians, aimed at people going about their lives who had no idea what was about to hit them."
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