Early results on Thursday from the Election Commission (EC) show the BJP almost certain to win one and possibly three of the states, with the Congress keeping only one.
The NDTV television said that based on early projections, the BJP was likely to win a two-thirds majority in the main state, Madhya Pradesh, and a narrow majority in the second most important, Rajasthan.
Early trends from the EC also showed the Congress retaining power in New Delhi and both parties in a close race in Chhattisgarh.
The Congress party has conceded defeat in Madhya Pradesh. "People have voted for a change, let there be change," Madhya Pradesh Chief Minister Digvijay Singh told reporters.
The BJP, on its part said it had no plans to call early national elections despite its strong gains in the state elections.
After Prime Minister Atal Behari Vajpayee met party leaders to discuss the state results, senior minister Arun Jaitley sought to quash speculation.
"Lok Sabha (parliament) elections will take place at the scheduled time," he told reporters. The national election is due in October, 2004.
Strong gains were expected to fuel pressure within the BJP to call national elections earlier than the due date.