The BJP is campaigning hard to hold on to UP
The contest there is widely predicted to be a tough battle for the BJP, which currently governs the state in alliance with smaller parties.
Voting also gets underway this week in Punjab, Uttaranchal and Manipur.
The BJP and its allies rule in Punjab and Uttaranchal while Manipur is under federal rule.
Results are expected by 24 February.
Poll repercussions
The Indian Prime Minister, Atal Behari Vajpayee, has attempted to play down the national implications of the state polls.
In comments to journalists on Monday, Mr Vajpayee said: "Where does the centre [national government] come into the picture?"
He said there were "no complaints" against the central government, and if there were any, they were against state administrations.
However, the UP Chief Minister, Raj Nath Singh, has warned that if the BJP loses control of the state, it could have international implications.
Hindu politics
Mr Singh said it would give Pakistan's President Pervez Musharraf the chance to say that the Indian prime minister was losing political support.
The regional Samajwadi Party is the main challenger to the BJP in UP, drawing support from lower-caste Hindus as well as Muslims.
Observers say the BJP is trying to win back support by appearing tough towards Pakistan.
But its appeal to nationalist sentiment has been complicated by demands by Hindu hardliners to press ahead with building a temple on the disputed Ayodhya site in UP.
The BJP wants to avoid a showdown over the issue in order not to fall out with some of its allies in the central government, who oppose the temple plans.