The unanimous opposition backlash against Ramesh Bidhuri – MP from prime minister Narendra Modi's Hindu-nationalist party – prompted the BJP chief to issue a show-cause notice.
Mr Bidhuri met BJP chief Jagat Prakash Nadda at the party headquarters in capital Delhi, days after he was asked to explain his behaviour in parliament.
Mr Bidhuri, 62, has been a member of the Lok Sabha (lower house of the parliament) and represents the elite South Delhi constituency. Critics of Mr Modi have raised concerns over rising hate against religious minorities and sectarian violence under the ruling party.
Mr Bidhuri targetted opposition MP Kunwar Danish Ali and called him a "terrorist" and "militant", while using other anti-Muslim slurs against him during a discussion on the success of India's Chandrayaan-3 moon mission last Thursday.
His remarks were later expunged from official records, but not before video from the discussion was shared widely and condemned on social media.
"When Danish Ali alerted me about what all Bhiduri had said, I immediately gave a ruling to expunge the unparliamentary words," said Kodikunnil Suresh, an MP from Indian National Congress, who was in chair at the time of discussion.
Lok Sabha speaker Om Birla reportedly warned Mr Bidhuri of possible strict action if he were to repeat such behaviour on the floor of the House.
Mr Ali in a letter to the speaker has sought a privilege action against the BJP lawmaker. He said: "During the course of his [Ramesh Bidhuri] speech he directed the most foul, abusive invectives against me which are part of the record of the Lok Sabha."
"This is most unfortunate and the fact that this happened in the new parliament and under your leadership as speaker is truly heartbreaking for me as a minority member of this great nation and an elected member of parliament."
Since the incident, the MP said he had been unable to sleep and was on the verge of a mental breakdown, according to NDTV. He threatened to quit parliament if Mr Bidhuri was let go without repercussions.
The opposition parties in a separate letter to the speaker have demanded Mr Bidhuri's suspension from the parliament till during the period of the Privileges Committee's investigation.
Adhir Ranjan Chowdhury, leader of the opposition in Lok Sabha, said expunging the "unsavoury words" had little impact since it had been already recorded in the media.
The leading Muslim bodies in India have also joined the demand for Mr Bidhuri’s disqualification, calling his remarks "evidence of hatred for entire Muslim community".
“The use of such language against a Muslim member of parliament shows that, let the common Muslims aside, now the elected representative of the Muslims is not safe even in the parliament," Jamiat Ulama-i-Hind president Arshad Madani said, according to The Hindu.
"If this is the picture of a new India, it is dangerous and disappointing.”