More than 127 million people are eligible to vote in this round of the seven-phase election held across 71 seats in nine states. The PM's coalition won more than 75 percent of the seats in the previous election in 2014.
Some of India's richest families, Bollywood stars and others voted early on Monday in Mumbai and elsewhere in the country as the fourth phase of a massive, staggered general election got underway.
Many of the constituencies are in Uttar Pradesh state in the north and western India's Maharashtra, where the financial capital Mumbai is located. Uttar Pradesh elects the most MPs, with Maharashtra next, and both states are ruled by Modi's Hindu nationalist Bharatiya Janata Party (BJP).
Mumbai-based journalist Neha Poonia reports.
However, political analysts say the BJP may struggle to repeat its strong showing this time due mainly to a jobs shortage and weak farm prices, issues upon which the main opposition Congress party has seized.
"Jobs should be the priority for the new government," said Aaditya Nair, a hotel management student, as he stood in line outside a polling station in Mumbai.
India's financial markets were closed on Monday for the election.
Mumbai, which has six seats, is India's wealthiest city but ageing and insufficient infrastructure is a major concern. Six people were killed last month when part of a pedestrian bridge collapsed, bringing back memories of a 2017 rush-hour stampede that killed at least 22 people on a narrow pedestrian bridge.
Mumbai is home to the massive Hindi film industry, as well as Asia's richest man, Mukesh Ambani, and India's richest banker, Uday Kotak.
Ambani, who heads Reliance Industries, and Kotak, managing director of Kotak Mahindra Bank, created a stir this month by publicly endorsing a Congress candidate from their upscale South Mumbai constituency.
The election, the world's biggest democratic exercise with about 900 million voters, started on April 11 with Modi in the lead amid heightened tension with long-time enemy Pakistan.
The last phase of voting is on May 19, with results released four days later.
There are a total of 545 seats in parliament's lower house.
Modi sent warplanes into Pakistan in late February in response to a suicide attack by Daesh that killed 40 Indian police in the disputed Kashmir region.
Modi has sought votes on his tough response towards militancy and in recent days has evoked the deadly Easter Sunday bombings in nearby Sri Lanka.
Maidul Islam, a professor of political science at Kolkata's Centre for Studies in Social Sciences, said long queues outside polling stations would indicate whether Modi's national security pitch was working.
"Whenever there is a BJP kind of a wave, you see a higher voter turnout," he said.