REUTERS - Millions of Indians began voting in the third round of a general election on Thursday in several states seen as key to the Hindu-nationalist Bharatiya Janata Party's bid to win power from the Congress-led ruling coalition.

The financial hub Mumbai began voting just months after an attack by Islamist gunmen that killed 166 people and inflamed tensions with nuclear-armed Pakistan, a security issue the BJP has used to criticise the government for being soft on terrorism.

The BJP appears to trail its main rival in a staggered, month-long election that could produce a weak coalition government as India grapples with the global economic slowdown and a spate of militant attacks in the past year.

More than 144 million people were eligible to vote on Thursday in a round that covers BJP strongholds in western and central India, as well as the insurgency-hit Kashmir valley. The BJP will hope to get a big haul in the western state of Gujarat where one of the party's biggest stars, the controversial chief minister Narendra Modi, is a poster boy for the party's campaign of development and good governance.

Both main parties may need the support of regional players to form a government after the world's largest democratic exercise, in which 714 million people from a myriad of castes, religions and ethnicities can vote, ends on May 13.

While India's main vote battle is between Congress and the BJP, a coalition of smaller parties known as the "Third Front" has an outside chance. That worries many investors who see the bloc as an unknown quantity if it comes to power.

The BJP needs to fulfil its potential in stronghold states such as Gujarat, Madhya Pradesh and Karnataka on Thursday to boost its chances of forging a winning coalition, said Swapan Dasgupta, a political analyst with links to the party.

OPPOSITION STRONGHOLDS

"All in all, it's a big day for the BJP. They're fighting in their strongholds or places where they feel they can make inroads," he said.

Manmohan Singh (Congress Party) AFP India’s prime minister since 2004 is considered the architect of the country’s financial reforms has a reputation as a ‘clean’ politician. Lal Krishna Advani (BJP)AFP The 81-year-old leader of the BJP is considered a hawk on India-Pakistan relations. His party advocates Hindu revivalism, but Advani has been trying to shed his hardline image. Mayawati (BSP) AFP Hailing from India’s low-caste Dalits, Mayawati is known as the "Queen of the Dalits." She could emerge as the leader of a “Third Front” of regional parties and rise in national prominence. But Mayawati faces a number of corruption charges and is criticised for her opulent tastes. Rahul Gandhi (Congress Party)AFP The son of Sonia Gandhi, Rahul Gandhi hails from prime Indian political stock. He is the son, grandson, and great-grandson of former Indian prime ministers. Sonia Gandhi (Congress Party)AFP The Italian-born leader of the Congress party gave up her chance to become prime minister in 2004 in favour of Manmohan Singh. Gandhi is the widow of a former Indian prime minister and is popular on the campaign trail. Narendra Modi (BJP°AFP The controversial chief minister of a western Indian state is criticised for his role in anti-Muslim violence in 2002. But Modi is a popular figure on the campaign trail and appeals to his party’s hardline base.

The BJP scored a narrow victory over Congress in Gujarat, which counts for 26 out of 543 seats in the national parliament and also hosts the constituency of its prime ministerial candidate L.K. Advani, in the last election five years ago.

Modi, tipped as a future party leader, is seen as the driving force behind Gujarat's economic success story and appeals to the party's large Hindu vote bank nationwide. The BJP will hope to build on what the business-friendly Modi achieved at state level.

But Modi's image -- and the BJP's -- may be tarnished as he is under investigation for allegedly turning a blind eye to some of India's worst ever religious riots in which some 2,500 people, mainly Muslims, died in Gujarat in 2002.

Maoist violence hit the first two rounds of voting in the April-May general election, killing more than 20 people as rebels targeted police and polling officials.

West Bengal state has deployed more than 19,000 paramilitary forces for Thursday's vote which covers three districts wracked by rebel violence.

Parts of the restive Kashmir valley vote amid a boycott call by separatists who do not want New Delhi to present a healthy turnout as Kashmiris' acceptance of Indian rule.

On Wednesday government troops locked down Kashmir's main city, Srinagar, the focus of a twenty-year insurgency.