"Modi should apologise for it as he insulted the people of Bihar," Rabri Devi, the former Bihar chief minister, said.
She said that Modi's words exposed the real character of Bharatiya Janata Party (BJP).
Even RJD chief Lalu Prasad has already made it clear that the grand alliance of JD-U, RJD, Congress and NCP will not tolerate insult to Nitish Kumar by Modi.
Besides, Raghuvansh Singh, a former union minister and vice president of RJD, said that Modi will have to apologise for his abusive words against Nitish Kumar.
"We want his apology, no less than it, "Singh said.
Interestingly, Nitish Kumar himself has not demanded an apology from Modi.
Kumar on Wednesday urged Modi to "consider taking back" his comments on his DNA.
After that, the BJP-led NDA leaders shot back by saying that "Bihar is not Nitish; Nitish is not Bihar".
But on Thursday, Kumar said: "I had made a request to the prime minister to take back DNA comments as it does not suit a man holding high constitutional post of prime minister."
The Janata Dal-United (JD-U) leader has raked up the DNA comment ahead of Modi's three proposed public meetings in Bihar this month.
In an open letter released on Twitter, Nitish Kumar said Modi's July 25 remark questioning his DNA was being seen as an "insult" by large sections 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.
"Therefore, through this letter, I take the liberty to urge you to please consider taking back these words.
Addressing a public meeting in Muzaffarpur, Modi had 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."