By Sethuraman N R and Devjyot Ghoshal

BENGALURU/NEW DELHI (Reuters) - Millions of voters across swaths of southern India cast ballots early on Thursday in the second phase of a mammoth, staggered general election, as sporadic violence flared in the east and the insurgency-wracked state of Jammu and Kashmir.

More than 155 million people are eligible to vote in 95 constituencies in 12 states on Thursday, with results of the election to India's 545-member parliament expected on May 23.

In focus are the southern states of Tamil Nadu and Karnataka, where the main opposition Congress party and its allies need to win big if they hope to stop Prime Minister Narendra Modi from securing a second straight term.

Modi and his Bharatiya Janata Party (BJP) have run an aggressive campaign, playing to their nationalist, Hindu-first base and attacking rivals they accuse of appeasing minorities.

Critics say such divisive rhetoric threatens India's secular foundations.

"Communal polarisation is the biggest issue for me," said Rakesh Mehar, who voted in the technology hub of Bengaluru, which is the capital of Karnataka. "And the growing intolerance in the country is what worries me the most."

Yet it may be tough for the BJP to repeat its 2014 feat of sweeping victories in six northern states that delivered 70 percent of all its seats, helping to clinch a landslide majority, said academic Neelanjan Sircar.

"You can never expect you’ll do that again," added Sircar, a political science professor at Ashoka University near the capital, New Delhi. "Those seats that you lose, you’ll have to make up somewhere."

The BJP would be looking to make gains in Karnataka, he added.

Congress, which is focusing on concerns about growing joblessness and farmers' distress, is staking its chances on a promise of generous handouts to India's poorest families.

"People are talking about national issues," said Manjunath Munirathnappa, a voter in Bengaluru, who hoped lawmakers would resolve infrastructure woes, such as traffic congestion and inadequate water supply.

"But only when they fix the local issues will there be progress."

SPORADIC VIOLENCE

The election, in which almost 900 people are eligible to vote, began last week and ends next month, with vote counting set for May 23 and results expected the same day.

Sporadic violence was reported in the northern state of Jammu and Kashmir, where separatists have called an election boycott and the eastern state of West Bengal, which has a history of election clashes.

Police fired teargas to disperse stone-throwers in Srinagar, the Himalayan region's main city, where thousands of troops had been deployed to guard the vote, although turnout was just 5 percent by 1 p.m.

"There has been stone pelting by protesters in at least 40 places," said a senior police officer who sought anonymity because he is not authorised to speak to the media.

Police in the West Bengal constituency of Darjeeling also fired tear gas at protesters who complained they had not been allowed to vote, said the top district official, Arvind Kumar Mina.

"They had blocked a highway and had to be dispersed," he added.

In the neighbouring constituency of Raiganj, unidentified people attacked the car of the communist candidate at a voting station he visited to check accusations of voting malpractice, the party said.

Elections in West Bengal have historically been marred by violence among the communists who ran the state for decades, the main opposition Congress and a powerful regional group, all trading charges of vote-rigging and intimidating supporters.

The election panel has banned campaigning for a few days by a firebrand Hindu ascetic from the BJP, who governs northern Uttar Pradesh, over his anti-Muslim comments.

(Reporting by Devjyot Ghoshal and Sethuraman NR; Additional reporting by Subrata Nagchoudhury in KOLKATA and Fayaz Bukhari in SRINAGAR; Editing by Sanjeev Miglani and Paul Tait)