The minister said the BJP has already been rejected by the people.
West Bengal Minister and state president of Jamiat-Ulema-e-Hind Siddiqullah Chowdhury on Sunday said Home Minister Amit Shah will not be allowed out of the airport whenever he visits the city, if the
Citizenship Amendment Act is not immediately withdrawn.
Mr Chowdhury said the contentious law is against humanity.
"We may not allow him (Shah) to step out of the city airport if necessary. We may gather one lakh people there to stop him," he said at a Jamiat-Ulema-e-Hind rally against the CAA.
Reacting to his remarks, BJP's West Bengal unit chief Dilip Ghosh told PTI that Mr Chowdhury has made such "provocative comments" in the past, too, with the "tacit support of Chief Minister Mamata Banerjee."
"How can a state minister issue such a threat? If they (Shah, PM Narendra Modi) are stopped from moving around in the city, then imagine the situation of others who don't share its (Trinamool Congress) views? Stop playing with fire," Mr Ghosh said.
The state's library service minister claimed that Jamiat-Ulema-e-Hind''s movement would be democratic and peaceful.
"We don't believe in violent protests, but we will certainly oppose CAA and the National Register of Citizens (NRC) tooth and nail," he said.
The minister said the BJP has already been rejected by the people.
"Just look at the ongoing protests all over the country, including in Kolkata," he said.
Mr Chowdhury, who addressed the rally at Rani Rasmoni Avenue, said the "56-inch chest" of PM Narendra Modi has let down the people of the country, as he is "pursuing the politics of hatred and division".
"What they (Modi and Shah) are doing is thrusting one agenda after another on the people. They don't believe in discussion, they don't believe in dialogue," he said.