Security had been tightened in a number of parliamentary constituencies across the north and north-east of the country .

The BBC Delhi correspondent, Daniel Lak, says, by the standards of past elections it has been a peaceful day.

BBC Delhi correspondent Daniel Lak: "With a low turnout nothing can be ruled out."

From the northern state of Bihar, where last week nearly 50 people died in attacks on police and election officials by Maoist militants, there were only scattered outbreaks of violence reported.

In the north-western part of the state several people were killed or injured in exchanges of gunfire between supporters of rival political parties.

Mr Vajpayee is confident of victory

In the remote north-east of the country, a few explosions were reported in the state of Nagaland, where separatist insurgents have been fighting Indian rule for more than 50 years.

The final result of the election will not be known until early October - but opinion and exit polls indicate a victory for the governing Hindu nationalist party, the BJP.

Voting also took place in Uttar Pradesh, like Bihar a crucial electoral battlegrounds. Together, the two northern states send 139 MPs to the 545-member parliament.

Candidate killed

Violence affected the third phase of voting

In the north-eastern state of Assam, a candidate of the Bharatiya Janata Party, who was kidnapped on Monday, was found dead on the eve of the poll.

Police officials say Pannalal Oswal, the candidate for the Dhubri parliamentary seat, had tried to strike a deal with rebels of the United Liberation Front of Assam (ULFA) to allow him to campaign freely.

But officials told the BBC that the rebels kidnapped him when he failed to pay them the Rs50m demanded from him.

The ULFA has called for a boycott of the parliamentary elections, but state government officials say candidates are being allowed to campaign if they pay the rebel group.

Uttar Pradesh

Voters queued for hours in Uttar Pradesh

The BBC's Satish Jacob says the BJP, which has done very well in Uttar Pradesh in the past few elections, is facing a strong challenge from a resurgent Congress party.

Uttar Pradesh was once a Congress stronghold. Many senior leaders - including Jawaharlal Nehru and Indira Gandhi - were elected to parliament from the state.