NEW DELHI — Narendra Modi, the man expected to become India’s next prime minister, swept into the capital on Saturday morning in a triumphal procession to the colonial bungalows here that still serve as India’s power center and promised that he “will try to make India self-reliant and strong.”

Mr. Modi, who engineered a historic victory over India’s long-governing Gandhi family, was surrounded at several places along the route by well-wishers who chanted paeans to him. When he stopped to greet the crowds, they showered him with rose petals.

Mr. Modi gave a brief speech at the headquarters of the Bharatiya Janata Party, which on Friday won a decisive majority in Parliament. It is the first time in India’s history that any party other than the Indian National Congress Party, led by the Gandhi family, has managed such a feat.

“I am thankful to you for the way in which you received me with so much gratitude from the airport,” Mr. Modi said.