The regional Samajwadi Party appears headed for a clean sweep – it has won 15 and is leading in another 200 seats. The state has 403 seats.
Congress also looks set to lose in Punjab, while it is engaged in a neck-and-neck contest in Uttarakhand state.
These polls are seen as a litmus test for the national elections in 2014.
They are also seen as a test for the Congress party-led central government, whose credibility has been eroded in recent months over a series of corruption allegations.
Manipur and Goa are the other states where counting is going on.
The most crucial of the state elections has been in the northern state of Uttar Pradesh, which has more than 200 million people.
Uttar Pradesh politics has been dominated in recent years by Mayawati, a low-caste Dalit who heads the Bahujan Samaj Party (BSP) and has had four terms as chief minister.
After all the hype about Rahul Gandhi leading a resurrection of the Congress party in Uttar Pradesh, the poll results there and in Punjab, Goa and Uttarakhand can only be termed as a major setback for the party’s national fortunes.
A victory in Manipur can’t make up for the setbacks in the other states.
Correspondents say the counts in Uttar Pradesh are a blow to the Congress party.
“The results are shocking. We are disappointed,” the state’s Congress party chief, Rita Bahuguna Joshi, told reporters.