Indians are voting in the sixth phase of a marathon general election in which the governing Congress party is fighting the main opposition BJP.
More than 180 million voters are eligible to vote in 117 seats in 12 states and union territories, including Tamil Nadu and Maharashtra.
The nine-phase vote began on 7 April and will conclude on 12 May. Votes will be counted on 16 May.
More than 814 million Indians are eligible to vote in the polls.
Election Commission officials say voter turnout in most states in the general election so far has been higher than in 2009.
Over 2,000 candidates are contesting Thursday's poll, which will also be held in the states of West Bengal, Uttar Pradesh, Madhya Pradesh, Bihar and Indian-administered Kashmir.
The southern state of Tamil Nadu, where voting will be held in all 39 seats on Thursday, is a key battleground.
The main contest is between two powerful regional parties - the ruling AIADMK and the main opposition DMK.
The two main national parties are fringe players in the state: the BJP has stitched up a six-party alliance and hopes to put up a challenge in some constituencies, while the Congress is fighting alone.
India's financial capital, Mumbai, will also vote on Wednesday in what promises to be a keenly-contested battle between two competing alliances: the ruling Congress-Nationalist Congress Party alliance is pitted against a resurgent BJP-Shiv Sena party.
Among the star candidates whose fates will be decided are BJP leader Sushma Swaraj, social activist and anti-corruption Aam Aadmi Party's Medha Patkar, former Bollywood actress and BJP's Hema Malini and the regional Samajwadi Party leader Mulayam Singh Yadav.
The marathon vote is being staggered over five weeks for security and logistical reasons.
The main contest in the election is between the Congress, led by Rahul Gandhi, and the BJP, led by the charismatic and controversial Hindu nationalist leader Narendra Modi.
Modi, who is ahead in all the pre-election opinion polls, is the leader of Gujarat state, which witnessed one of India's worst anti-Muslim riots in 2002.
The BJP has promised to improve the economy and curb corruption if it wins.
The Congress party has promised "inclusive growth" if it returns to power, with a raft of welfare schemes, including a right to healthcare for all and pensions for the elderly and disabled.
The anti-corruption Aam Aadmi (Common Man's) Party, which secured a spectacular result in local polls in Delhi last year, offers a challenge to the main parties.
Several smaller regional parties are also in the fray and if no single party wins a clear majority, they could play a crucial role in the formation of a government.
Any party or a coalition needs a minimum of 272 MPs to form a government.