Saturday's New Delhi legislative elections pit Modi's Bharatiya Janata Party against the incumbent Aam Aadmi Party, or "common man's" party, whose pro-poor policies focused on fixing state-run schools and providing cheap electricity, free health care and bus transport for women during its five years in power.
Modi and Home Minister Amit Shah appealed to majority Hindus by focusing on national issues such as the citizenship law, which triggered widespread protests, at the expense of problems facing the capital's millions of residents.
At least 23 people were killed in clashes between police and protesters against the law in December.
With counting of votes almost complete, the Aam Aadmi Party, or AAP, had won 52 seats and was leading in another 10 of the 70 constituencies, while the BJP had won six seats and was leading in another two, the Election Commission said. The Congress party, led by Sonia Gandhi, was unlikely to win any seats.
Full results were expected later Tuesday.
The defeat was a setback to Modi's prestige, coming less than eight months after he led the BJP to a resounding victory in national elections. The party won all seven of the capital's parliamentary seats in those polls.
The victory was a major boost for AAP chief Arvind Kejriwal, the 51-year-old incumbent New Delhi chief minister and anti-corruption crusader.
Kejriwal joined hundreds of his supporters in celebrating the party's performance. In a brief speech. he said the election "has given birth to a new brand of politics — politics of development'' to meet people's basic needs.
Modi in a tweet congratulated Kejriwal for his party's victory. "Wishing them the very best in fulfilling the aspirations of the people of Delh," he saidi.
Local BJP leader Manoj Tewari denied the AAP accusation that his party had tried to create a Hindu-Muslim divide during the elections. Hindus comprise more than 80% of India's 1.3 billion people and Muslims about 14%.
Kejriwal launched his party in 2012 and campaigned to rid the political system and government of corruption and inefficiency.
The party's symbol — a broom— and its promise to sweep the administration of graft struck a chord with New Delhi nearly 20 million people.
In the 2015 elections, Kejriwal's party won 67 seats and the BJP three.
Modi and Home Minister Shah campaigned vigorously in an attempt to unseat the AAP and capture power in New Delhi. The BJP last ruled New Delhi in the 1990s.
The new citizenship law fast-tracks naturalization for non-Muslim migrants from neighboring Pakistan, Bangladesh and Afghanistan who are living in the country illegally. The BJP also hoped to garner Hindu votes for ending the semi-autonomy of Muslim-majority Kashmir last summer and turning the disputed region into two federally governed territories.