Among high-profile candidates who cast votes early was former UN diplomat Shashi Tharoor in the southern city of Thiruvananthapuram.
"It is a great privilege to vote. It is an extra bonus to vote for myself," said Mr Tharoor, who is standing for the Congress party. "I should be able to romp home."
In Andhra Pradesh state there were reports of a very high turnout.
But the BBC's Sanjoy Majumder in Varanasi in Uttar Pradesh says voter levels there were disappointing, despite a brisk start.
Our correspondent says the poor turnout was being blamed on very hot weather as well as anger at both the choice of candidates and the poor record of elected representatives.
A massive security operation is in place across India for the ballot and at least 17 people have been killed in attacks blamed on Maoist rebels.
In the eastern state of Jharkhand seven security personnel and two civilians were killed in a landmine blast blamed on the rebels, police said.
There were more than a dozen other incidents where insurgents attacked polling stations, kidnapped voting officers and fought fierce gun battles with security forces.
The BBC's Damian Grammaticas is at a polling station in Chhattisgarh state
In the neighbouring state of Bihar, Maoist rebels attacked a polling station in Gaya district, killing two security personnel and injuring two women before making off with the electronic voting machines and a number of weapons.
The rebels also triggered a landmine explosion in Jamui district and in Rohtas, police told the BBC more than 50 Maoist rebels attacked a police station and fought Border Security Force personnel.
In Orissa's Malkangiri district, insurgents burned some electronic voting machines, police said. The rebels also blocked roads in the district after felling trees.
The first day of voting took place in constituencies spread across the country, including volatile areas in north and central India.
The states where voting took place were Andhra Pradesh, Arunachal Pradesh, Assam, Bihar, Jammu and Kashmir, Kerala, Maharashtra, Manipur, Meghalaya, Mizoram, Nagaland, Orissa, Uttar Pradesh, Chhattisgarh, Jharkhand, Lakshwadeep and the Andaman and Nicobar Islands.
More than two million security personnel have been deployed for the poll. Many are on duty in the southern state of Andhra Pradesh, which has been voting for both national and state assembly representatives.
Thousands of troops have also been on alert in the northern state of Uttar Pradesh, which has the most seats in the national parliament.
Polling in phase one took place for 16 of the state's 80 seats.
Neither of the two main parties in the election - Congress and the Bharatiya Janata Party (BJP) - is expected to gain a clear majority.
Both may have to depend on the support of smaller parties to form a government - and correspondents say the campaign rhetoric in recent days has become increasingly bitter.
Security is a key election issue, especially after last year's attacks in Mumbai (Bombay), but the global economic meltdown and local and regional affairs are also sure to be important.
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