In an RSS workers meet in Bihar yesterday, Bhagwat had said that the Sangh would "prepare military personnel within three days which the Army would do in 6-7 months."
This also exposes the RSS's "hidden agenda to float parallel militias to wreak havoc, crush national unity", he said in a Facebook post.
"RSS chief Mohan Bhagwat's comments on the Indian Army are in poor taste, against constitutional propriety, confirms our worst fears about the Sangh that it has no respect for India's institutions," the chief minister said.
The RSS chief must apologise to the people of India for this "treacherous" remark, the chief minister said.
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Vijayan also demanded that Prime Minister Narendra Modi clarify his government's position over Bhagwat "belittling" the Indian Army.
The RSS chief had also said, "This is our capability. Swayamsewak will be ready to take on the front if the country faces such a situation and Constitution permits (to do so)."