An alliance of regional parties took 178 seats out of 243. The BJP won 58.

Mr Modi won a convincing victory in last year's national elections, but this poll was seen as a referendum on his economic programme.

Defeat is a major setback for the prime minister, says the BBC's Sanjoy Majumder, in Delhi.

However, a spokesman for the Hindu-led nationalist BJP rejected suggestions the result was a personal blow for Mr Modi, saying the party "managed a creditable performance".

The prime minister had been hoping a victory in Bihar would boost his party's strength in India's upper house of parliament, which is made up of representatives of state legislatures and where he lacks a majority.

With a population of 100 million, Bihar is one of India's largest states and one of the poorest.

The BJP's defeat in Bihar is the second consecutive setback for Narendra Modi's Hindu nationalist party since it swept to power in Delhi last year.

Earlier this year the BJP suffered a drubbing at the hands of an upstart anti-corruption party in Delhi. Now a "grand alliance" of powerful regional parties has handed out a defeat in what is one of India's most politically crucial states.

Despite what his defenders say, Sunday's defeat is another blow to the charismatic Mr Modi, who is arguably the party's biggest vote-getter and who attended 26 campaign rallies in Bihar ahead of the vote. The results make it clear that Mr Modi's vote-catching abilities are on the wane and voters are already holding him to the promises he made to them last year.

For India's bedraggled opposition, the Bihar victory is a major shot in the arm. They will now be emboldened to challenge Mr Modi by forging alliances and change the narrative of Indian politics.

-BBC