MUMBAI, India — He does not act the part. At 76, Subramanian Swamy has a youthful demeanor, is frequently cheeky but is almost always composed. Yet he is arguably the most vicious infighter in Indian politics, where he has spent a career of more than 40 years taking down ministers and governments. Lately, he has been on a roll.

First, he drove out India’s central bank chief.

Next he set his sights on the chief economic adviser to the Finance Ministry.

Then he made a veiled attack on the finance minister for wearing a business suit on a trip to China instead of traditional Indian garb, saying he looked like a waiter.

In the process, Mr. Swamy, an economist, has become the subject of intense controversy, an unapologetic Hindu nationalist whose antics are increasingly threatening the stability of the government of Prime MinisterNarendra Modi. Now, the question is whether Mr. Modi will be able to keep him on a tight enough leash to prevent him from cannibalizing his government.

Before his latest forays, he was “the chief wrecker” of the government in 1999, under Prime Minister Atal Bihari Vajpayee, causing its fall after 13 months, said Sudheendra Kulkarni, a close adviser to Mr. Vajpayee.

“They’ll face the worst consequences” from tolerating him, Mr. Kulkarni said. “He’ll be a great spoiler.”

Not only has Mr. Modi tolerated Mr. Swamy, he has actively promoted him, rescuing him from the political wilderness by elevating him to a seat in the upper house of Parliament. The reason, political observers say, is Mr. Swamy’s value as one of India’s most effective fighters against the country’s endemic corruption, something that Mr. Modi has made a centerpiece of his plans to modernize and invigorate India’s economy.

“If Modi is going to live up to his promise to clean up government, he needs Swamy,” said Madhav Das Nalapat, a former editor of The Times of India and a friend of Mr. Swamy’s.

In an interview in his New Delhi office, where one wall is covered with pictures of himself with Indian leaders of recent decades, Mr. Swamy declared his latest attacks had the support of “senior colleagues in the party” and were made only after they “told me, ‘You are absolutely right.’ ”

The son of a government bureaucrat, Mr. Swamy was raised in New Delhi but left in 1962 to pursue a doctorate in economics at Harvard, the beginning of a nearly 50-year affiliation with the university, as an associate professor and summer lecturer.

In 1969, after obtaining his degree and teaching at Harvard for several years, he returned to India, hoping to build an academic career there. But as an outspoken advocate of free-market economics, he found himself shut out of the intelligentsia, then rabidly leftist.

Unable to find a permanent place in India’s top academic institutions, Mr. Swamy was contemplating a return to the United States when he fell in with a Hindu nationalist group, the Rashtriya Swayamsevak Sangh, the ideological parent of the governing Bharatiya Janata Party.

“My critics began saying I was a chauvinist, nationalist, mad nationalist,” Mr. Swamy said, prompting the Hindu nationalist group to begin wondering, “ ‘Who is this guy who is speaking our language and we don’t even know him?’ ”

The group offered Mr. Swamy a seat in the upper house of Parliament in 1974. He took it, beginning his career in politics.

Over the years, Mr. Swamy has served five terms in Parliament for two different parties that have since become part of Mr. Modi’s governing party. He settled into a routine of spending winters in India and summers teaching at Harvard.

His Harvard chapter came to an abrupt end in late 2011, when he wrote a newspaper article after a series of militant attacks in Mumbai. The article called for the demolition of 300 mosques, some built over temples, and argued that Muslims should be barred from voting in India unless they acknowledged their Hindu ancestry. The article led Harvard’s faculty to cancel his summer course offerings.

Mr. Swamy, in an interview, was unapologetic about the article and restated his theory of Muslims in India being descended from Hindus. He added that he wished the Harvard faculty had at least given him a chance to make his case before canceling his courses.

Few who know him say they believe he is really anti-Muslim, suggesting that his comments are aimed at building a support base among Hindu nationalists. “Swamy is a closet secularist,” Mr. Nalapat said. “Otherwise, how do you explain his family?”

Mr. Swamy’s wife, Roxna, is a member of the Parsi community, which emigrated centuries ago from Iran. One of his sons-in-law is Muslim.

Whatever his role in Hindu nationalism, Mr. Swamy has been a force behind some of India’s landmark corruption cases. He petitioned the Supreme Court in 2010 to prosecute the telecommunications minister at the time over his involvement in awarding cellphone spectrum to companies below market rates. That helped fuel the perception of widespread corruption and led to the defeat of India’s longtime governing Congress Party.

He also brought a lawsuit against several Congress Party leaders, including Sonia Gandhi, its president, and Rahul Gandhi, her son and the party vice president, accusing them of illegally acquiring a newspaper for its real estate assets and forcing them to show up in a New Delhi courthouse as the accused and post bail.

“Everyone thought that nothing could nail the Gandhi family,” said Sanjaya Baru, a onetime spokesman for former Prime Minister Manmohan Singh. “Swamy showed it’s possible.”

Lately, Mr. Swamy has taken his battles beyond the courthouse to social media, where he has nearly three million Twitter followers. He typically rises at 4 a.m. and, over a cup of coffee, unleashes a torrent of attacks on the platform. Before turning in at night, he sends out another round of bullets from his Twitter gun.

In April, as the question of whether Raghuram G. Rajan would continue as central bank governor was being debated, Mr. Swamy leapt into the mix. In an open letter to the prime minister, he accused the bank governor of an “apparently deliberate attempt to wreck the Indian economy” by refusing to lower interest rates, which would have made it cheaper for small and medium-size companies to get loans.

Not content to attack Mr. Rajan on interest rates, a genuine policy choice, Mr. Swamy also questioned his loyalty to his country. Citing the bank governor’s possession of a United States green card, allowing him to work and reside there, Mr. Swamy suggested that Mr. Rajan was “mentally not fully Indian.”

Mr. Rajan has not publicly commented on his decision to step down, but his parents told the newspaper The Indian Express that their son had been hurt by the attack — and the government’s failure to rise to his defense.

Mr. Swamy is convinced that without his attack, Mr. Rajan “would have gotten an extension,” because he had supporters and it would have been easy to follow the path of least resistance and allow him to stay in the job.

Mr. Rajan’s departure seemed to energize Mr. Swamy, who found a new target in Arvind Subramanian, the Finance Ministry’s chief economic adviser. Dredging up testimony before a United States congressional committee from several years earlier, in which he was critical of India’s policy on intellectual property, Mr. Swamy again raised questions about loyalty and tweeted, “Sack him.”

Within days, he also posted on Twitter what appeared to be an attack on the finance minister, Arun Jaitley. Minutes after Mr. Jaitley appeared on Indian television dressed in a suit and tie on a visit to China, Mr. Swamy posted: “BJP should direct our Ministers to wear traditional and modernised Indian clothes while abroad. In coat and tie they look like waiters.”

Later, as the Indian news media reported increasing unease in the Bharatiya Janata Party about his comments, he protested that he had not been referring to Mr. Jaitley, who looked “very smart in a coat.”

Four days later, Mr. Modi, in a rare interview on Indian television, denounced Mr. Swamy’s attacks as inappropriate and publicity stunts, saying, “the nation won’t benefit from such behavior.” Too late for Mr. Rajan and his supporters, he rose to the central bank governor’s defense, saying, “I believe Raghuram Rajan’s patriotism is no less than any of ours.”

If Mr. Swamy was chastened, he showed no signs of it. On Twitter, he made fun of Mr. Modi’s interviewer and fired off some new attacks on the Gandhi family.