"All the names that have come up, the reports that are coming, so the probe is very essential...it is the violation of government's rules and regulations, so we demand a joint paramilitary committee on this," Karat told reporters in West Bengal's Siliguri district.
Meanwhile, in Hyderabad, former Telugu Desam Party (TDP) president Chandrababu Naidu joined the CPI (M) in demanding JPC probe against the controversy, which he said has shamed the nation.
"This is a national shame and all of us have to take the responsibility. Even country has to face the guilt all over the world; everybody is thinking what is happening in India. On one side we are talking that India will become a developed nation and it will be among top three nations," Naidu said.
"India will become one of the biggest and efficient democracies of the world. We are facing this type of problem, so the government of India has to come out," he added.
As for the IPL commissioner Lalit Modi, who is being pressurised to resign in the wake of the controversy has tweeted that he is not going to quit.
"People pressurising me to resign - I can tell you will not happen. Let them remove me then," Modi put out his message on Twitter.
Income tax officials are carrying with their raid in offices of IPL franchisees following the charges of corruption against the IPL tournament.