Akayed Ullah, the 27-year-old suspected bomber, had a crude pipe bomb strapped to his body. The device exploded prematurely on Monday between two subway platforms near Port Authority, injuring him and three others.
Bangladesh security officials said that they have found no evidence of a local terrorist link to Ullah despite his fascination to Islamist literature.
"We have not found any link between Akayed Ullah and local terrorist groups or any political party. We have not found any clue of his affiliation with any terrorist outfit in Bangladesh," police counter-terrorism unit chief Monirul Islam told reporters here.
His wife told investigators that Ullah used to "encourage" her to read books by a convicted Islamist outfit chief Jashim Uddin Rahmani as he appeared to have been radicalised over the internet after moving to the United States, he said.
"She said he used to tell her to read the books of Jashim Uddin Rahmani to learn about religion or Islam. We are reviewing the information provided by his wife and other relatives," Mr Islam said.
Rahmani, the leader of the outlawed Ansarullah Bangla Team (ABT), was jailed by a Bangladesh court in 2015 for five years for inciting the murder of atheist blogger Ahmed Rajib Haider in Dhaka.
His books were easily accessible on the internet until some years ago.
The ABT is a homegrown extremist group which is behind the killings of several bloggers, writers and gay rights activists in Bangladesh.
Mr Islam said that though no official request has been made, Bangladesh passed on the information on Ullah to US security agencies on its own as "we have given highest priority on this issue because of our zero-tolerance policy against terrorism".
An official familiar with the investigation said Ulllah's wife was "surprised to find out what her husband did" after he exploded a pipe bomb strapped to his body which he did some 30 minutes after his routine telephonic talks with her.
Bangladesh police's counter-terrorism unit questioned her and other relatives for several hours.
Police said that Ullah, who became a US resident in 2011, visited Bangladesh three months ago and spent most of the time at home with their six-month-old son.
Ullah is suspected of trying to blow himself up at New York's main bus terminal presumably inspired by Islamic State ideals while investigators are trying to unearth what led to the bombing, and who - if anyone - might have assisted him.
His improvised explosive device, however, did not work as intended, causing minor injuries to bystanders.
Authorities took the suspect into custody alive and later brought federal charges against Ullah, who has so far appeared to be the lone wolf in plotting and staging the attack.