NEW DELHI—Exit polls suggest Prime Minister Narendra Modi, the nationalist leader who has dominated Indian politics since he swept into power in 2014, could get another five years leading the world’s largest democracy.

Mr. Modi is immensely popular among Indians who see him as a strong leader who is making the country—especially the Hindu majority—proud. But critics have questioned his steering of the economy and worry he and his supporters could use another big win as a mandate to push the country in a less tolerant, less...