The accused, Palash Bose, had claimed himself to be a member of Dawood Ibrahim's gang while making these phone calls, ATS officials said.
A Kolkata resident, arrested on Friday for allegedly making threatening calls to Shiv Sena MP Sanjay Raut, had also made similar calls at residences of Maharashtra Chief Minister Uddhav Thackeray, state home minister Anil Deshmukh and NCP chief Sharad Pawar, ATS officials said on Saturday.
The accused, Palash Bose, had claimed himself to be a member of Dawood Ibrahim's gang while making these phone calls, they said.
An official said Bose (49) had lived in Dubai for more than 15 years and returned to Kolkata a few years ago.
"He made these calls by using a SIM card which he had procured from Dubai," he said, adding that Bose told investigators that he had also used international SIM cards to make these calls.
Police are trying to find out if Bose had any connections in Dubai, the official said.
Kolkata Police had said on Friday that a team of Mumbai Police nabbed the accused from his Tollygunge residence for allegedly threatening Raut earlier.
Bose had allegedly used internet calling services to call and threaten the Shiv Sena MP with dire consequences earlier this month.
Raut had lodged a complaint following which Mumbai Police tracked the man's IP address and located him in Kolkata.
During his arrest, Mumbai Police sleuths also seized the device allegedly used by him to call Raut and issue threat.
Mumbai Police were given the transit remand of the accused till September 14.
On Sunday, police had beefed up security outside Thackeray's residence "Matoshree" in Bandra after an unidentified caller, claiming to be fugitive underworld don Dawood Ibrahim's aide, called the bungalow's landline number.
State Home Minister Anil Deshmukh had received threat calls on more than one occasion over his stance in connection with the controversy involving actress Kangana Ranaut.
Deshmukh had received the calls from Himachal Pradesh and another location from different numbers on Tuesday and at around 6 am on Wednesday, sources close to him had said, adding that the callers asked the minister not to get involved in the controversy.
Earlier also, an anonymous caller had phoned Deshmukh's Nagpur office, threatening him and NCP chief Sharad Pawar, a minister had said.
The Shiv Sena and the actress are engaged in a war of words after the latter recently likened Mumbai to Pakistan- occupied Kashmir (PoK) and also said she feared Mumbai Police more than the movie mafia.The Brihanmumbai Municipal Corporation (BMC), which is ruled by the Shiv Sena, on Wednesday pulled down some illegal alterations made at Ranaut's bungalow in suburban Bandra. The Bombay High Court later granted a stay.