They believe the murder might have been carried out by an IS sympathiser and not necessarily by active members of the radical group.
"There has been no concrete evidence of IS' direct presence in Bangladesh,” India’s leading newspaper Times of India quoted an intelligence official as saying in a report published on its website on Wednesday.
“But the country does have a worrying proliferation of radical Islamic groups who pose a clear terror threat. The killing of the Italian may have been a lone-wolf attack by an IS sympathiser," the official told the newspaper.
Bangladesh Home Minister Asaduzzaman Khan Kamal earlier in the day told reporters that primary investigations into the murder “negated” the involvement of IS in the incident.
He claimed that even Italian authorities did not think it was an IS job.
The murder did not have the IS hall mark of beheading the victim.
According to forensic report, Tavella was shot thrice from behind at close range.
The incident in Dhaka, however, has alerted the Indian agencies who anticipate similar lone-wolf attack in the country.
"There is a clear and present danger of a radicalised individual or group, swayed by IS' ideology of violent extremism, attempting a lone-wolf attack in India.
"The agencies are alert and are pro-actively tracking such suspect elements, especially their online exchanges, and intervening the moment they betray signs of joining the IS or travelling to Iraq/Syria," a senior officer told the TOI.