The R.B.I., an agency akin to the Federal Reserve in the United States, has said little about why it decided that Indian financial data must be stored only in India. In its April order, it said, “In order to ensure better monitoring, it is important to have unfettered supervisory access to data stored with these system providers.”

Its policy changed as other arms of the Indian government — spurred by both a privacy ruling from the Supreme Court and India-first nationalists in the governing Bharatiya Janata Party — had begun deliberating over much bigger changes to the country’s data, e-commerce and privacy laws.

Those broader proposals, which are unlikely to be passed until after India’s national elections in May, are intended to curb the ability of American tech titans to collect, analyze and make money from data they collect inside the country, which is the world’s fastest-growing market for new internet users. The rules would also give a leg up to domestic firms like Reliance Jio, a leading telecom provider, and Paytm, a payments company, which are seeking government help as they try to compete with the likes of Google, Facebook, Amazon and Mastercard.

India’s prime minister, Narendra Modi, has portrayed himself abroad as a pro-business leader who welcomes foreign investment. At the same time, the right wing of his party has pushed him to adopt more protectionist, India-first policies to appeal to voters, and law enforcement officials have urged him to make sure they can easily get data on residents when they need it.

The Trump administration and the bipartisan India caucus of the United States Senate have both urged India to reconsider its data localization campaign, in part because India’s own outsourcing companies depend on moving data across borders to offer their services.

On Friday, the co-chairmen of the India caucus, Senators John Cornyn, Republican of Texas, and Mark Warner, Democrat of Virginia, wrote to Mr. Modi warning that data localization “will have negative impacts on the ability of companies to do business in India, may undermine your own economic goals and will likely not improve the security of Indian citizens’ data.”