Mr Adams was initially declared a "person of interest", but the investigation now permits him to be referred to as a suspect, multiple outlets reported.
Speaking to NBC's TODAY show on Wednesday morning, New York Mayor Eric Adams said police are still "zeroing in" on the suspect. Mr Adams urged commuters to remain vigilant when riding the subway.
Security cameras at the subway station were not operating during the attack, hindering the investigation, The New York Times reported.
Besides unexploded bombs, petrol, a fuse, a hatchet, expended ammunition clips and a gun, police found the key to a rented U-Haul van, which was linked to Mr James’s address.
The Federal Bureau of Alcohol, Tobacco, Firearms and Explosives is trying to trace the origin of the weapon, which was fired 33 times at passengers as smoke filled the train.
Authorities said Mr James had made a number of social media posts that appeared to threaten violence. One video made before the attack said he was “heading into the danger zone”.
Several posts by Mr James made references to violence and pervasive racism, also threatening black people and speaking about committing violent acts, and railing against Mr Adams.
“This nation was born in violence, it’s kept alive by violence or the threat thereof and it’s going to die a violent death. There’s nothing going to stop that,” Mr James said in one video.
Police Commissioner Keechant Sewell called the posts “concerning" and officials tightened security for Mr Adams.
Members of the public have been offered a $50,000 reward for information leading to Mr James's arrest.
Mr Adams, a former NYPD captain, has pledged to address some of the root causes of crime since being sworn in as mayor in January.
New York's crime rate increased by 36.5 per cent in March versus last year, with shooting incidents rising by 16.2 per cent compared to a year ago, police statistics showed.
Survivors describe Brooklyn subway attack
One passenger, Jordan Javier, thought the first popping sound he heard was a book dropping. Then there was another pop, people started moving toward the front of the car, and he realised there was smoke, he said.
When the train pulled into the station, people ran out and were directed to another train across the platform. Passengers wept and prayed as they rode away from the scene, Mr Javier said.
“I’m just grateful to be alive,” he told The Associated Press.
The attack could revive memories of a time when New York suffered a wave of violent crime on its subway system.
In the 1980s, New York City’s subways were a symbol of urban disorder: graffiti-covered, crime-plagued and shunned by tourists.
Like the rest of the city, though, the subways have cleaned up their act in recent decades. Before Covid-19 hit, the main problem with the trains was not crime but overcrowding and breakdowns related to ageing infrastructure.
More than 3 million riders have taken the subways in recent days, according to Metropolitan Transit Authority estimates.
After the September 11 terrorist attacks, New Yorkers learnt to live with the worry that the subways or other parts of the city could be a target for terrorists.
In 2017, an ISIS sympathiser blew up a pipe bomb strapped to his chest in a subway station near the Port Authority Bus Terminal, injuring several bystanders.
Christopher Herrmann, a former city police officer who is now a professor at John Jay College of Criminal Justice, said episodes such Tuesday's shooting are bound to provoke a new round of anxiety, especially among people who use the subway.
“With 9/11, you have a specific target: the World Trade Centre,” Mr Herrmann said. “A lot of people can wrap their heads around that.”
But the seeming randomness of this week's attack “really invokes a lot of fear and worry,” he said, “because most people don’t consider themselves a target”.
The MTA announced on early Wednesday that several trains running from the 36th Street station resumed service in each direction.
Agencies contributed to this report.