The latest provocation is Mr Aiyar saying in Karachi that while most political parties in Pakistan want cordial relations with India, those in India are "still caught in a partially 1947 situation".
"All political parties except the Jamaat-e-Islami say they want peace with India. Now this change in mindset that is taking place in Pakistan is not reflected in India," Mr Aiyar said.
His comments came two days after Pakistan-based terrorists attacked an Army camp in Jammu, killing six soldiers and one civilian and injured 10 people, including women and children. Defence Minister Nirmala Sitharaman warned on Monday that "Pakistan will pay for its misadventures".
"Mani Shankar Aiyar should stop giving such remarks, he has already been suspended. He should stay quiet," said Mr Rao told news agency ANI, adding, "I am writing to Rahul Gandhi ji asking him to expel Aiyar from the party."
Mr Rao worried that Mr Aiyar's remarks - he called them "weird" - can damage the party's prospects in Karnataka, where assembly elections will be held soon. "The BJP can take advantage of this," Mr Rao fumed, also stating, "He has earlier given such kind of a wrong statement during the Gujarat election campaign and we have suffered a lot because of that. Later Congress president Rahul Gandhi ji even suspended him but still he said that I have got lot of love and affection from Pakistan. What nonsense is he really talking about?"
The BJP's Sambit Patra said Mr Aiyar is a "repeat offender," pointing out that "we have seen him in the past also going to Pakistan and saying 'Modi ko hatana hoga'."
Just before Gujarat voted in assembly elections in December last, Mr Aiyar had called PM Modi a "neech aadmi," a comment that earned him a reprimand and a suspension order from Rahul Gandhi.
But the damage was done and the BJP did not let the Congress forget it for a moment thereafter. PM Modi said Mr Aiyar had insulted not him but his entire home state of Gujarat and urged voters to punish the Congress.
The Congress posted its best performance in Gujarat in years, narrowing the margin, but it was the BJP that won the state for the fifth time in a row. Mr Aiyar's self goal was seen to have played a considerable role in that result.
And not for the first time. Ahead of the 2014 national election Mani Shankar Aiyar had derided Mr Modi as a tea seller who could never be Prime Minister. In his campaign, Mr Modi offered his credentials as a self-made leader, stressing that he sold tea on trains as a young boy to help support his family and contrasting his modest origins with those of the Congress' Gandhi family.
In the BJP's sweep of the 2014 elections, Mr Aiyar was seen as having made significant contribution.
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.