Telecast by a Bengali news channel, Trinamool's Bankura district head Arup Chakraborty is seen in a video clip asking his partymen to "sacrifice whoever intrudes your homes".
"If any outsider enters your house, cut him down, sacrifice him, I will take care of that, you don't have to worry," Chakraborty is seen in the video telling his party activists in Bankura.
Paul, who represents Krishnanagar Lok Sabha constituency in West Bengal's Nadia district, was caught on video warning Communist Party of India-Marxist (CPI-M) men to "beware" of him as he won't "spare you and destroy your entire clan" and "unleash my boys to rape your women".
His remarks have drawn widespread criticism, with people across political lines and activists seeking his arrest.
Several Trinamool leaders have in the past been in the eye of the storm for their hate speeches.
Trinamool's Birbhum district chief Anubrata Mandal has been accused in a murder case when a panchayat member was killed allegedly days after he asked his party workers to "attack the houses of rivals and bomb the police if they prevent you".
Infamous for his hate speeches, Mandal earlier likened CPI-M activists to "rats hiding in burrows".
"The rats are now hiding in their burrows, you should pit the burrows with mud and also use cyanide so they don't come out," Mandal told a party rally.
Party legislator from Labhpur in Birbhum district, Manirul Islam was in the news for publicly claiming he crushed to death three people under his feet and for threatening to behead a Congress leader from the district.
"...it would not take me even a minute to behead you," Islam said at a rally last year and went on to claim how he had "squashed" three people under his feet for committing atrocities against women.
This is not the first time Paul has made a hate speech. Addressing an election rally in Nadia district earlier, he asked party workers to "beat up" CPI-M workers and drive them out of the villages.