Police said they were looking for Frank R James, 62, in connection with the attack as he had rented a U-Haul van that may be linked to the shooting.
The key to the van, rented in Philadelphia, was found at the scene.
“We are looking to determine if he has any connection to the train,” NYPD Chief of Detectives James Essig said.
The New York Police Department (NYPD) asked “anyone with information on his whereabouts” to call a hotline.
Mr James has not been named as a suspect in the attack. Being identified as a person of interest means police believe he may have information concerning the crime.
The New York Times reports that Mr James, who has addresses in Wisconsin and Philadelphia, appears to have posted dozens of videos on social media in recent years, in which he expresses bigoted views. More recently he had also criticised New York City Mayor Eric Adams.
In a briefing late on Tuesday, police gave more details of the incident which saw a male attacker detonate two smoke grenades and open fire at Brooklyn’s 36th Street station.
The attack unfolded shortly before 08:30 local time (12:30 GMT) on Tuesday, and police said the man had a Glock 9 mm semi-automatic handgun.
“He then fired that weapon at least 33 times, striking 10 people,” police chief Mr Essig said. Seven men and three women were shot.
Images from the scene showed bloodied passengers lying on the floor of the smoke-filled station.
Another 13 people “suffered injuries related to smoke inhalation, falling down or a panic attack”, the police chief said.
All of the victims are expected to survive.
“The male then fled the scene, and detectives are actively trying to determine his whereabouts,” Ms Essig said.
Investigators found the Glock handgun, three extended magazines, a hatchet and a range of potential incendiary devices at the scene.
A $50,000 (£38,450) reward is being offered for information leading to the arrest of the suspect.
Police say the gunman was roughly 5ft 5in tall and 170lb (77kg). He was said to be wearing a construction vest, grey hooded sweatshirt, and a gas mask.
The attacker’s motive was not immediately known.
New York City Police Commissioner Keechant Sewell said earlier on Tuesday that the shooting was not initially being treated as an act of terrorism.
Witnesses have described hearing people shouting for medical assistance and fleeing in panic. Brooklyn resident Yayha Ibrahim said he saw people running from the 36th Street station.
“I saw a lady, she was shot right in her leg and she was screaming for help,” he told Reuters news agency. Rescue workers “did a good job of coming quick and fast, and the ambulance came in and they took her”, he added.
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“My subway door opened into calamity. It was smoke and blood and people screaming,” eyewitness Sam Carcamo told the Associated Press. He added that a billow of smoke poured out of the train once its doors opened.
Initial police investigations into what happened may have been hampered by a failure in the station’s surveillance system.
“At that particular station there appeared to be some form of malfunction with the camera system,” Mayor Adams later said.
Responding to the attack, President Joe Biden expressed gratitude to “all the first responders who jumped into action, including civilians who didn’t hesitate to help their fellow passengers.”
US cities have seen a rise in gun violence over the past two years.
“This insanity that is seizing our city has to stop,” New York Governor Kathy Hochul said after the attack. “We say no more. No more mass shootings. No more disrupting lives.”