Around 100 text messages were sent to politicians, including Union Minister Shashi Tharoor, from two mobile numbers procured using forged documents in the past fortnight.
Police has detained one more person in connection with the incident.
Out of the 100 messages, around 40 were sent on April 13 and 14, including the ones to Tharoor, MPs Brinda Karat, Mehmood Masood Madani, Rashid Alvi, Om Prakash and Sandeep Dikshit, police sources said.
Investigations have revealed that one of the two connections procured using the documents of a gym instructor Manick Verma was later transfered to another name using different set of identification papers.
Police detained one more person, who is identified as Yashpal, as investigators found that identification papers belonging to him were used in one of the SIM cards procured and used for sending "threatening" and "filthy" text messages.
A senior police official said they were now on a "process of elimination" to zero in on the suspect.
"We have zeroed in on some people. We are calling more people for questioning. Details cannot be shared as it will hamper the investigations," he said.
Police had earlier found that documents in the name of a city-based gym trainer were used by an unknown person to procure a SIM card from which "malicious" and "threatening" messages were sent to Tharoor and others.
Verma's SIM came under scrutiny after Tharoor's Officer on Special Duty (OSD) Jacob Joseph received an SMS two days ago claiming to be from the 'henchmen' of Karachi-based underworld don Dawood Ibrahim. The SMS threatened the Minister to stay out of IPL Kochi team or face death.
Police sources said, Verma told investigators that a police team from Sonepat had come to his west Delhi residence recently in connection with a probe into a "filthy" SMS sent from the same number.
However, after questioning Verma, an instructor at the Constitution club gym, it emerged that he was not at fault and his documents were being misused.