The outfit, Vedanta Shanskriti Moncho, also asked all pro-liberation forces to show black flag to Banerjee if she visits the country.
"We think the (Islamist) militants are carrying out anti-Bangladesh and anti-Indian activities at the indulgence of West Bengal Chief Minister Mamata Banerjee...She is yet to open her mouth on the matter though the peace-loving people of both the countries are talking about the issue," the organisation's general secretary, Binoy Bhushan Joybhar told a press conference here.
The organisation alleged that operatives of banned Bangladeshi outfits took refuge in West Bengal in the face of intensified security clampdowns and Banerjee continued to shelter them despite Dhaka's repeated requests against it, endangering peace and sovereignty of both the countries.
The outfit urged Modi not to include Banerjee in his entourage during his Dhaka visit from June 6 while it welcomed him.
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Banerjee will visit Dhaka on June 5 and join the Prime Minister who will formally sign the Land Boundary Agreement along with Bangladesh Prime Minister Sheikh Hasina the next day. She will return on June 6 after the signing of the agreement.
"It is her (Mamata) desire and so we arranged her accommodation at the Radisson Hotel," a foreign ministry official told media.
The West Bengal chief minister earlier said she would come to Dhaka to witness the Land Boundary Agreement as during her previous Bangladesh visit in February this year Banerjee said she played her part in the ratification of the 1974 treaty.