BJP leader Amit Shah said the party would form governments in Uttar Pradesh, India's most populous state, where early counting showed it had won an overwhelming victory, as well as in Goa, Uttarakhand and Manipur.
Modi battles for hearts and minds in India's holy city
"This is a historic mandate by the people of these states for BJP," he said at a press conference at the party's New Delhi headquarters.
"These results will set Indian politics in a new direction."
India's Election Commission is due to announce the final results later Saturday, but early counting shows the BJP leading in four out of five states where elections have been held over the past two months.
The opposition Congress Party retained power in just one state, northern Punjab.
Shah said the results were a defeat for "dynastic politics", in an apparent jibe at Congress, led by Sonia Gandhi and her son Rahul.
"The people have accepted the politics of performance," he said, promising that the faith they had placed in the party and in Modi would be rewarded.
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