The BJP also picked up support in Uttar Pradesh and is set to get half the seats in the heartland state which sends the largest number of lawmakers to parliament, according to the ABP News-Nielsen poll forecast, published on Saturday.
The results present a challenge to Rahul Gandhi, the fourth generation member of the long-ruling Nehru-Gandhi dynasty, who is leading the ruling Congress party-led coalition in national polls due by May.
About 57 per cent of respondents in the survey, conducted in February, picked Modi as their favourite candidate for prime minister, four points more than in the agency's January survey.
Gandhi trailed with a rating of 18 percent, though he picked up three percentage points from January.
The poll predicted the BJP and its allies would win 236 of 543 seats at stake in parliament's lower house, while the Congress and its allies would drop to double-digits.
More than 800 million people are eligible to vote in the world's largest democratic exercise to choose a new government. India, Asia's third largest economy, is growing at its slowest clip in a decade, choking off employment opportunities for thousands of young people who join the workforce each month.
To rule, a party needs the support of 272 lawmakers. The BJP, even with the biggest number of seats, will have to seek out coalition partners if the poll's predictions are correct.
In Uttar Pradesh, which accounts for 80 seats, the BJP was estimated to win 40, up five from the January poll. The Congress party was expected to win seven seats, a drop of one from last month's forecast.
More than 29,000 people across the country were interviewed for the poll. Local opinion polls have had a mixed record in the past, given the country's huge and diverse electorate.
Gandhi has struggled to draw support for the Congress party, which is mired by corruption scandals and policy paralysis. He has seemed distant at times, unsure of how to stop the slide in the 129-year-old party's fortunes.
Compared with the relatively untested Gandhi, Modi has years of experience as the chief minister of the western state of Gujarat, where he has built a reputation as an efficient, business-savvy administrator.
But charges that Modi was complicit in riots in Gujarat that killed at least 1,000 people, most of them Muslims, have cast a shadow over his ambitions for the top job. Critics accuse him of not having done enough to stop the violence, allegations he has strenuously denied and have never been proven.