But early surveys carried by India media outlets put the ruling United Progressive Alliance (UPA) led by the Congress party ahead of the main opposition National Democratic Alliance (NDA) headed by the BJP.
Exit polls have had a mixed record in the past, given the difficulty of projecting election results for India's approximately 1.1 billion people.
The counting of actual votes will begin early on Saturday, with the final tally expected to be released later the same day or early on Sunday.
Voting on Wednesday took place in the states of Tamil Nadu, Himachal Pradesh and Uttarakhand besides the remaining seats in Punjab, Uttar Pradesh, Jammu and Kashmir and West Bengal.
The two union territories of Chandigarh and Pondicherry also went to the polls on Wednesday.
Al Jazeera's Barnaby Phillips, reporting from the state of Punjab, a relatively prosperous part of India with a predominantly Sikh population, said voters had turned up early, eager to cast their ballots.
But "there are also hardships in Punjab. We have been hearing how the terrible problem of farmers' suicides has spread to this part of India," he said.
"Many of these people have been telling us prices just keep on going up and up, and that they are sinking into debt. That is going to affect how they vote.
According to the Indian constitution, a new parliament must be in place by June 2.
The final verdict is expected to trigger a frantic round of political horse-trading as the two main blocs scramble for new partners among a multitude of regional parties, all with their own local agendas.
"Everything will depend on numbers," Manmohan Singh, the Indian prime minister, said at a news briefing on Monday.
The Congress party, which has been in power for the past five years, has seen its main achievement of a robust economic growth hit by the global economic crisis.
The party also faces severe criticism for its handling of the Mumbai attacks in November, when 10 armed men - allegedly from Pakistan - rampaged through the city, killing 166 people.
|The Indian elections are the world's largest exercise in democracy [AFP]
Nonetheless, Abhishek Manu Singhvi, a Congress party spokesman, said the party was confident of forming a coalition government.
"Whether individually or collectively we know very well how to conduct coalition ethics," he said, adding that they have the necessary experience to "do it successfully".
For its part, the BJP says it is confident of wresting power and ruling the country together with its allies for the next five years.
Many of the seats are expected to go to a range of regional and caste-based parties that tend to focus on local issues and promises, leaving India facing the prospect of a shaky coalition.
Observers say that whatever formation emerges it will most likely be an unwieldy coalition that will struggle to project a united front at a time when India is facing a sharp economic downturn and numerous foreign policy challenges.