In an open letter, Nitish Kumar said Modi's comment had been taken as an "insult" by a large section of the people of the state and beyond.
"Most of us feel that these statements, beyond questioning my own descent, have disrespected the lineage of our people and have denigrated the great legacy of the state," he said.
"This also gives credence to the feeling that perhaps you and your party hold a prejudice against the people of Bihar.
"Therefore, through this letter, I take the liberty to urge you to please consider taking back these words.
"I have no doubt that this gesture of yours would go a long way in assuaging the sentiments of the people and would further enhance the respect people have for you," he said.
Addressing a public meeting in Muzaffarpur on July 25, Modi said: "There seems to be some problem in his (Nitish Kumar's) DNA because the DNA of democracy is not like that. In democracy, you give respect even to your political rivals."