Modi said Aiyar's remark testified to the Congress's "Mughal mentality".
The prime minister also said the Congress leadership cannot digest if someone from a humble background "wears good clothes", an apparent retort to Rahul Gandhi's "suit-boot ki sarkar" jibe.
"One leader in Congress comes from a very learned family. He himself was an officer of the Indian Foreign Service and also a minister in the Congress government.
"Shriman (Mr) Mani Shankar Aiyar today said that Modi is of 'neech jaati' (low caste) and is 'neech' (vile). Is this not an insult to Gujarat? This is an insult to the great legacy of India. This is born of Mughal mentality," he told an election rally here in poll-bound Gujarat.
Earlier in the day, Aiyar said, "He (Modi) is 'neech kism ka aadmi' (a vile man) who has no 'sabhyata' (civility)."
Aiyar's controversial comment came after Modi accused the Congress of seeking votes in B R Ambedkar's name but trying to erase his contribution to nation building.
"You called us donkey, you called us 'gandi nali ka kida' (worm of a dirty drain), you called us 'maut ka saudagar' (merchant of death), you said I am of 'neech jaati' and 'neech'. But we will live according to our 'sanskars' (values)," Modi said.
Modi said people of Gujarat had seen his 14 years as chief minister and then prime minister.
"Have I done anything which made you look down in shame? Have I done any 'neech' work?" Modi asked the crowd which responded with the chant of "Modi! Modi!".
The prime minister said he may belong to a low caste but his values were such that he always did (uchha) good work.
He said he followed in the footsteps of Mahatma Gandhi and worked for the uplift of the poor. "I sit with those who are most backward, I work for their uplift, I follow the principles of Mahatma Gandhi. You may call me 'neech' for that, but I will continue on this path," Modi said.
The prime minister requested his followers and BJP workers not to respond to Aiyar's remarks "even on Twitter".
"I request all BJP workers and followers who believe in values in public life with folded hands... do not say even a word against those who have used such language against me, against the prime minister of this country, against son of Gujarat, even on Twitter," he said.
"But if you have any anger over the use of such words against me, press the button alongside the lotus symbol on 9th and 14th (Gujarat polling dates)," Modi told the gathering.
He said Gujarat will teach a lesson to the Congress on December 18, the day votes would be counted.
When results come out, you will know the gravity of the word you used, Modi said.
"The Congress party has lost its mental balance as it knows it is going to lose this election. Could anybody imagine that they will lose Assam? They have lost Uttar Pradesh, Maharashtra, Uttarakhand and also Bihar. The entire country has discarded them," Modi said.
He said, the Congress had forgotten public decorum after a string of disappointing losses in these states.
"Gujarat has endured many insults. They called me 'maut ka saudagar'. They tried to put me behind bars, they tried to jail half of my cabinet," Modi said, adding despite being the prime minister for three-and-a-half years he never took a single step with a feeling of vengeance.
"That is not my way. We are ones who uphold decorum in public life," Modi said.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)