The statement is not an isolated one but a reflection of the "racist and communal" mindset of the present BJP dispensation, the parties said.
Vijayvargiya, who is the BJP national general secretary and its Bengal minder, had courted controversy on Thursday by stating that he had found the eating habits of some of construction labourers working at his house in Indore "strange" as they were eating only `poha' (flattened rice).
He had said it had roused his nationality and after talking to their supervisor and the building contractor he suspected that they were from Bangladesh.
Senior TMC leader and state Minister of State for Parliamentary Affairs Tapas Roy said such racist and communal statements are reflection of BJP's "anti-Bengali" mindset.
"We all know that BJP is an anti-Bengali party. Such communal statements only reflect that mindset. BJP and its leaders don't know anything about Bengal, its culture and eating habits and are dreaming of ruling Bengal. They would get a befitting reply for insulting Bengalis," he said.
Roy's view were echoed by CPI(M) Politburo member Mohammed Salim, who alleged that BJP is trying to do a racial profiling of the country.
"Just because someone is not eating roti does not make him a Bangladeshi. Poha, which is known as chirey in this part of the country, is a staple diet and is very popular as breakfast food. What is BJP trying to do? They are trying to racially profile the country on the basis of dress code, eating habits and lifestyle," Salim said.
He also said Vijayvargiya's comments are "just an extension" of Prime Minister Narendra Modi's remark that those indulging in violence over the citizenship law could be identified by their attires.
Modi, while addressing a rally in Jharkhand in December had said people who had set ablaze property during anti CAA protests can be identified by the clothes they wore.
Leader of Congress in the Lok Sabha, Adhir Ranjan Chowdhury too criticised Vijayvragiya sand said his comments are an "insult to the people of West Bengal".