In an open letter to the PM, which was released on social media sites Facebook and Twitter, Kumar said the comment was "unbecoming" of the office he holds.
"Your words have been taken as an insult by a large section of the people of the state and beyond. Most of us also feel that coming from you, the comment is rather unbecoming of the office you hold," he said.
Kumar's view was shared by Congress, a partner in Bihar.
Congress leader Renuka Chaudhry said in Delhi, "PM should not have said so. He should immediately withdraw the comment as he is no more a pracharak."
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Though no word has come from the PM so far, senior Bihar BJP leader Sushil Kumar Modi reacted to the JD(U) leader's charge and clarified that the PM meant to refer to "Kumar's political DNA."
"Kumar, who is now in the company of Congress, probably is confused that he is Bihar like Congress leader D K Barua who had said 'India is Indira and Indira is India'," Sushil Modi, who was deputy chief minister during the NDA regime, told reporters.
"Nitish Kumar's DNA is that of betraying friends and allies whereas the DNA of Bihar represents harmony and welcoming a guest with dignity.
"DNA of Bihar does not teach anybody to snatch a plate from in front of a guest after calling him for dinner," he said referring to Kumar cancelling a dinner for BJP leaders in 2010 to express anger over advertisement in newspapers highlighting donation given by then Gujarat Chief Minister Narendra Modi for rehabilitation of Kosi flood victims.