Addressing hundreds of thousands of mainly Hindu supporters at a rally in the northern state of Uttar Pradesh, Modi said his economic policies meant Muslims were better off in Gujarat, the western state he governs, than other parts of India.
The rally in the state capital Lucknow, where a third of the population is Muslim, was attended by a sea of people clad in orange, the colour associated with Hinduism. The ground, which can hold some 400,000, was not totally full.
Modi, 63, has a strong lead in opinion polls ahead of the regionally phased general election voting due in April and May, but the surveys suggest he may still struggle to gather enough seats to form a government. Muslim votes could help.
"We believe in economic development, while you play the politics of votes, letting Muslims languish in poverty," Modi said, in a jibe at the government of Uttar Pradesh, which relies on Muslim support and has a poor development record.
Modi is dogged by allegations he did not stop religious riots in Gujarat over a decade ago, when at least 1,000 people, mainly Muslims, were killed in retaliation for the death of Hindu pilgrims in an attack on a train.
He denies the allegations and a Supreme Court inquiry concluded there was not enough evidence to try him.
Modi's comments were his most direct attempt to woo Muslim voters since being named last year as the candidate of his Bharatiya Janata Party (BJP) or prime minister.
Hindu-Muslim relations have been a central part of Indian politics for centuries. The Hindu nationalist BJP made its name 20 years ago by whipping up tensions between the communities.
Because of that history, most Indian Muslims are still wary of Modi, but some are convinced by his message of economic development for all.
"We want people to unite, if that happens, India will be much more prosperous and more secure for Muslims," said Amir Uddin, a scholar of Islam sporting a "Modi for PM" cap who travelled 200 km in a BJP bus to attend the rally.
Muslims are among the most economically deprived sections of Indian society. Hindus make up about 80 percent of India's population while Muslims account for some 13 percent.
Modi's message is unlikely to win over Muslim voters in droves, but it may help convince other Indians who are drawn to his strong economic record but fear he is a divisive leader.
His speech came just a few days after BJP President Rajnath Singh made conciliatory remarks to Muslims, saying the party was ready to apologise for mistakes it may have made. He called on Muslims to give the BJP a chance.
FOCUS ON ECONOMIC RECORD
Singh also struck a soft note on Sunday, making reference to Lucknow's religious tolerance in the 18th and 19th centuries under its Muslim Nawab rulers, who built a famous Hindu temple in the city.
Modi has roots in hard line pro-Hindu politics, but he has focused his election campaign almost entirely on his economic achievements in Gujarat, which has witnessed double-digit economic growth for a decade.
He has the strong support India's corporate sector and investors, who hope he will replicate Gujarat's economic model on a national scale.
On Sunday, Modi contrasted tension between religious communities in Uttar Pradesh, which has seen dozens of riots in the past two years, with a period of peace in Gujarat.
BJP leaders blame the spate of riots in Uttar Pradesh on the state government, run by the regional Samajwadi Party, but concede privately that the resulting polarisation has helped their party draw Hindu voters.
Dates for the general election are likely to be announced next week. A new government must be formed by the end of May.