In February, the Indian authorities arrested Vikram Kothari, a ballpoint pen magnate, saying he had diverted loans given to his company by seven government-owned lenders. He also denied wrongdoing.

The allegations against Mr. Modi have only strengthened people’s wariness of the state banks. Indian officials have publicly accused him of working with tellers at a single branch of one of them, Punjab National Bank, to obtain $1.8 billion from branches of other banks. So far, five Indian banks have been swindled in the scandal, four of them government-owned, the authorities in New Delhi say.

Just a decade ago, during the global financial crisis, Indian lenders were held up as a bastion of stability. Today, they are considered more vulnerable than those in other leading emerging markets, mostly because state-controlled lenders dominate the sector, according to the International Monetary Fund.

Of the $6.5 billion in fraudulent loans that have hit the industry over the past two years, the most egregious cases were at government-owned banks, according to figures released by Parliament. Executives at those lenders are more likely to be appointed for their political connections than for their talent, financial analysts say.