The New York Times and other media quoted police sources as saying the suspect had told investigators he had carried out his attack in response to calls by the Islamic state.
He added that he chose the subway tunnel linking the famous Times Square with the port authority station because of the existence of numerous television screens and posters of the attacks that were carried out in the name of the jihadi organization and targeting German markets in Germany, according to the same sources.
The suspect also wanted to retaliate against US strikes against the organization of the Islamic state in Syria and other countries, the New York Times said, quoting sources.
Police said the bomber was a 27-year-old Bangladeshi immigrant named Aqadeedullah, who lives in the Brooklyn neighborhood and was carrying an "improvised explosive device" that appeared to have exploded prematurely.
The explosion took place at 7:20 pm (1220 GMT) at a rush hour in a subway tunnel connecting two important transport hubs, Times Square and the Port Authority's land transport station, not far from 42nd Street and Eighth Avenue in the city.
Police said the suspect was arrested and taken to hospital for "injuries and burns to his body" after the explosive device that was attached to his body.
Three people at the scene were slightly injured, the authorities said.
According to the White House, the Bangladeshi migrant arrived in the United States in 2011 after receiving a visa for reunification.