Voting in the world's largest democracy is phased over several weeks, and will end on May 12. Results are due to be announced on May 16.
The opposition Bharatiya Janata Party, headed by Modi, has benefitted from a wave of public anger over corruption scandals and a slowing economy under the ruling Congress Party.
Although the polls have repeatedly indicated that the BJP will emerge as the largest single party in the 543-seat lower house of parliament, it is unlikely to win an outright majority, and is seen as most likely to form a coalition government.
The BJP and its allies are forecast to claim 36 percent of the popular vote in Uttar Pradesh, which as India's most populous state offers the largest number of parliamentary seats, according to a poll published by CNN-IBN and Lokniti at the Centre for the Study of Developing Societies (CSDS) late on Thursday.
That would give the BJP and its partners between 42 and 50 seats - up slightly from the 41 to 49 seats scored by the BJP in a February survey - and more than half of the 80 seats contested, the poll showed.
The Congress Party and its allies, meanwhile, are forecast to pick up just 16 percent of the popular vote, down 3 percent from February, giving them only a handful of seats as Congress looks on track for its worst-ever electoral performance.
Elsewhere, the BJP and its partners are predicted to perform well in the large states of Rajasthan and Maharashtra, where they may get 55 and 43 percent of the vote respectively and the largest number of seats, according to two CNN-IBN-Lokniti polls.
The CSDS will reveal national results of its polls later on Friday, the last major poll to be published before voting begins.
Elections in India's sprawling democracy are notoriously difficult to predict, and translating vote share into actual seats won is not always reliable.
To collect the data for the polls, Lokniti at the CSDS conducted face to face interviews with 20,957 voters spread across 21 states between March 18 and March 25.
Polls have consistently shown voters favouring Modi, a divisive but charismatic figure, to lead the country.
Whereas Rahul Gandhi, the political heir of the Nehru-Gandhi dynasty appointed to lead the Congress campaign, has struggled to gather support among voters.