NEW DELHI (REUTERS) - India's ruling Bharatiya Janata Party was heading for election defeat in New Delhi at the hands of an anti-corruption party, a TV projection showed on Tuesday, in the first blow for Prime Minister Narendra Modi since he swept to power last year.

Winning power in India's states is critical to control of the upper house of parliament, where Modi's party lacks a majority and has been thwarted in its effort to move reform legislation, including wider opening of the insurance sector.

But Delhi is a small, although high profile, state and the BJP, which has won a string of big states over the past several months is looking to capture power in second most populous Bihar, the next state set for an election later this year.

The Aam Admi, or Common Man Party, campaigning on pro-poor policies, was leading in 45 of the 70 seats at stake in the capital, well over the simple majority of 36 required to rule.

The BJP, seen as a party of traders and big business, was ahead in 15 seats while Congress, which ruled Delhi for 15 years, led in 3 seats. News channel NDTV said its projection showed the AAP would finally win 42 seats, securing a comfortable majority.

"While Delhi is not very significant in electoral terms, a BJP loss there shatters the popular narrative around the BJP's invincibility," said Milan Vaishnav, an associate at the Carnegie Endowment for International Peace.

"A loss in Delhi certainly signals an end to Modi's honeymoon. Furthermore, because it is the capital city, an opposition government, especially one led by the confrontational AAP, would be a constant thorn in the Modi government's side."

The BJP said the Delhi election was a local poll and in no way reflected its strength in the rest of the country. "This is not a referendum on the central government," said party spokesman G.V.L.Narasimha Rao.