Winning the elections would be a major coup for Prime Minister Atal Bihari Vajpayee, since his Bharatiya Janata Party (BJP) and its allies have won just four major state elections since he was elected in 1998.
The Election Commission said Bharatiya Janata led in Rajasthan, Madhya Pradesh and Chhattisgarh, which were previously controlled by the opposition Congress party. Congress was ahead only in the state of New Delhi.
The BJP may have been helped by recent peace initiatives with rival Pakistan, including a cease-fire in disputed Kashmir and the resumption of air links. The economy, expected to grow by 7% this year, may also have played a role.
Yesterday, Mr Vajpayee went a step further, sending a letter to his Pakistani counterpart to say he will take part in a regional summit in Islamabad next month, Press Trust of India reported.
India had refused to attend a meeting of the South Asian Association for Regional Co-operation in January. The association can only convene if all members India, Pakistan, Bangladesh, Sri Lanka, Bhutan, the Maldives and Nepal agree to attend.
Pre-election surveys had predicted victory for Congress in New Delhi, Rajasthan and Chhattisgarh. However, exits polls from the vote on Monday suggested the BJP had recovered a lot of ground.
The latest counting showed that in Madhya Pradesh, the BJP had won 127 of 230 seats and led in the race for 39. Congress won 21 seats and led in 17 districts, while smaller parties and independent candidates were ahead in the remaining seats.
Congress' top elected official in that state, Digvijay Singh, conceded his 10-year rule had ended.
"People have voted for a change," he said. "There is a wave in favour of the BJP."
Congress clearly won New Delhi state. But in Rajasthan, BJP won 115 of the 200 seats so far, according to the Election Commission. Congress had 54 so far. Venkaiah Naidu, president of BJP, met with Mr Vajpayee and senior party leaders. They sought to quash speculation that the good showing would encourage the BJP to call early national Parliament elections.
"I don't see the possibility of an early general election," said Arun Jaitley, the government's law minister.