The central government, however, dismissed allegations of any kind of surveillance on its part on specific people, saying it "has no concrete basis or truth associated with it whatsoever".
Sawant said in Maharashtra, a case of alleged "unauthorised phone-tapping" by (senior IPS officer) Rashmi Shukla during the previous Devendra Fadnavis-led government has already come to light.
"But, there were also reports of the use of Pegasus software," he claimed.
The Congress leader asked if any IPS officer in the state headquarters 'Mantralaya' (secretariat) was working on this.
"With whose permission did officers of the DGIPR (Directorate General of Information and Public Relations) go to Israel? What training did they receive? Did they come back and report? Is it related to Pegasus?" he asked.
Sawant said it is "surprising and suspicious" that such tours took place during the election period (in 2019).
He said the issue of phone tapping at the national level through Pegasus software and the "probable role of the Modi government in it is a very serious matter" in the country.
All BJP-ruled states may have been instructed to work on this procedure, he claimed.
"Phone tapping during the Fadnavis government in Maharashtra had the same intentions," he alleged.