In a setback, Indian Prime Minister Narendra Modi's ruling party has decided not to form the government in the western state of Maharashtra - the country's richest - leaving opposition groups scrambling on Monday to cobble together an alliance.

The Bharatiya Janata Party (BJP) emerged as the single largest part in a state election in Maharashtra last month, and was expected to comfortably retain power with the help of its regional ally, the Shiv Sena.

But in-fighting between the BJP and the Shiv Sena, which has gone on for a fortnight, has culminated in the allies parting ways, dealing the first major political blow to Modi's ruling party since it retained power with a landslide mandate in a May general election.

On Sunday, the BJP's state president Chandrakant Patil said his party had decided to not stake claim to form government.

Shiv Sena, which is still officially part of a ruling alliance led by the BJP, is now trying to form a government in Maharashtra with support of opposition parties, a senior party official said on Monday.

"We have required numbers to form the government and we will prove it," the Shiv Sena official said, declining to be named. In a tweet on Monday, the Shiv Sena's Arvind Sawant, the federal Minister of Heavy Industries and Public Enterprises, also quit from Modi government.

Whereas the BJP and Shiv Sena share Hindu nationalist sentiments, Shiv Sena's political base in Maharashtra is the Hindu Marathi community.

Maharashtra - home to India's financial capital Mumbai - has a 288-member assembly, meaning Shiv Sena, which won 56 seats, will need the support of other parties to be able to come to power.