AHMEDABAD, India—Two 29-story steel-and-glass office buildings rise above a dusty wasteland in the Indian state of Gujarat, the most conspicuous sign of progress on an ambitious project conceived by the man who is now India’s prime minister, Narendra Modi.

More than seven years ago, Mr. Modi, at the time the state’s top elected official, decided to push the construction of an entirely new city—dubbed the Gujarat International Finance Tec-City, or GIFT—about a 40-minute drive from Ahmedabad, the historic commercial hub here.

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