Aiyar had earlier in the day attacked the prime minister for saying that the Congress tried to erase the contribution of BR Ambedkar in nation-building. The Congress has a different culture and heritage.
The Gandhi scion said, "I do not appreciate the tone and language used by Mr Mani Shankar Aiyer to address the PM. Both the Congress and I expect him to apologise for what he said", Gandhi said.
"They called us donkeys, neech, gandi naali ke keede...the people of Gujarat will give a befitting reply to such derogatory language".
Prasad alleged that Aiyar targetted Modi because the latter had questioned the delayed conferring of Bharat Ratna - the countrys highest civilian award - on Dalit icon Ambedkar and Sardar Vallabhbhai Patel.
Aiyar, while talking to ANI, said it was the first prime minister of India, Pandit Jawaharlal Nehru, who turned Dr Ambedkar's wish into reality and it was not correct to badmouth the Nehru-Gandhi family.
Senior Congress leader Aiyar on Thursday called PM Modi "neech" (low) for critiquing the Congress even while inaugurating Ambedkar International Center at New Delhi. "This is an insult to Gujarat".
Speaking to media, Aiyar said: "My mother tongue is not Hindi and I do not use any filthy words".
"Yes, I used the word "neech". In one of his first tweets, the PM said: "I have nothing to say on a "wise" Congress leader calling me "Neech". But in Hindi if low means low-born, then I tender apology", he told reporters after his remarks in the morning triggered a political storm. "As far as I am concerned the bulk of my remarks dealt with Modi's very, very nasty remarks about the Congress, particularly with Gandhi's relationship with Ambedkar". The prime minister also accused the Congress leadership of having a "Mughal" mindset.
The prime minister said he has "nothing to say" to say to such people, and his answer to them will "reflect through the ballot box".