Much attention was focused on Mumbai, the capital of Maharashtra, which is ruled by an uneasy combine of the regional Shiv Sena and the Bharatiya Janata Party, who have struggled since their heavy defeat in national elections.
Singh said that price rises caused by the poor monsoon would soon be reversed and he reassured voters that "the worst is indeed over".
However, LK Advani, the BJP leader, accused Singh of corruption during campaigning.
"Corruption is the cause of price rises and the prime minister had failed to check the corruption," he said.
"Polling is going on peacefully all over the state except for ... one incident," AN Roy, the police officer overseeing election security in Maharashtra, told NDTV news channel, referring to a Maoist attack.
Maoists and police exchanged fire near a polling booth in their forested stronghold of Gadchiroli in Maharashtra, where they killed 17 police officers last week.
Vital concerns in Maharashtra range from improving security after the Mumbai attacks last year in which 166 people died, the recent slowdown in economic growth, and rural poverty that has led to a series of farmer suicides.
Haryana state, near to Delhi, the capital, is a well-populated agricultural and industrial region, while Arunachal Pradesh in the mountainous northeast borders China.
Beijing said on Tuesday it was "seriously dissatisfied" by Singh's visit to Arunachal Pradesh, the latest tense exchange between the neighbours over border areas claimed by both.
Singh travelled to the state earlier this month to woo voters.
Ma Zhaoxu, China's foreign ministry spokesman, accused an unnamed Indian leader of ignoring China's concerns by visiting Arunachal.