The sharp comments come in the middle of a standoff in parliament over the Manipur crisis.
Prime Minister Narendra Modi today slammed the opposition as "directionless" and cited the "Indian Mujahideen" and "Popular Front of India" as he derided the opposition alliance for its new name, INDIA.
"I have never seen such a directionless opposition," BJP leader Ravi Shankar Prasad quoted the Prime Minister as saying at the weekly meeting of the BJP parliamentary party.
PM Modi also attacked the opposition grouping on the name it gave itself at a meeting of 26 parties in Bengaluru last week to discuss strategy for the 2024 national election - INDIA, an acronym for Indian National Developmental Inclusive Alliance.
"They keep praising themselves for the name INDIA. Indian National Congress. East India company. Indian Mujahideen. Popular Front of India - these are also INDIA. Just using the name INDIA does not mean anything," Mr Prasad quoted the Prime Minister as saying.
People cannot be misled merely by the use of the country's name, he said.
BJP chief JP Nadda also took a swipe at the newly formed opposition coalition. "There was a child who failed in all his exams. He was hated by his classmates and neighbours. So the parents thought of changing his name to change his perception. Isn't the case similar to that of I.N.D.I.A?" Mr Nadda tweeted.
The sharp comments come in the middle of a standoff in parliament over the Manipur crisis and repeated disruptions over the opposition's demand for a statement by PM Modi on issues like a viral video of two women paraded naked by a mob and assaulted in May.
The Prime Minister described the opposition as "defeated, tired, hopeless, with a single-point agenda - opposing Modi". Their conduct showed they had made up their mind to remain the opposition, PM Modi reportedly said.
He expressed confidence that the BJP would win the 2024 polls easily with people's support.
Hours later, Congress leader Rahul Gandhi, one of the leaders involved in naming the opposition alliance, responded to the PM's comments. "Call us whatever you want, Mr. Modi. We are INDIA. We will help heal Manipur and wipe the tears of every woman and child. We will bring back love and peace for all her people. We will rebuild the idea of India in Manipur," he posted on Twitter.
The row over Manipur has stalled the government's plans to push key legislation in parliament. Both houses of parliament have been adjourned repeatedly without much business since the monsoon session started last Thursday, a day after the Manipur horror video emerged.
In his remarks before the session, PM Modi said his heart was filled with anguish and anger. "I want to assure the nation, no guilty will be spared. Action will be taken according to the law. What happened to the daughters of Manipur can never be forgiven," he said.
The opposition, debuting in this session as the "INDIA" coalition, said the Prime Minister must make a comprehensive statement in both house of parliament. The government, which has offered a discussion on Manipur in both houses, accuses the opposition of deliberately blocking legislation with its protests.