India's main opposition Bharatiya Janata Party (BJP) won nine seats and was leading in two others in the Hindu-dominated Jammu region. The People's Democratic Party won 11 and India's ruling Congress party won eight.
"We are open to an alliance with Congress," Omar Abdullah, the president of the National Conference, told Reuters news agency.
Despite a boycott call by separatists, more than 60 per cent of Kashmiri voters participated in the elections.
The voting was also relatively peacefully compared to previous polls.
Separatists in Kashmir, claimed by India and Pakistan but ruled in part by both, say New Delhi portrays voting as an endorsement of its rule over the Himalayan region.
Overall violence has fallen significantly across Kashmir since India and Pakistan began peace talks in 2004, although New Delhi has "paused" the dialogue since last month's Mumbai attacks blamed on a Pakistan-based group.
Officials say more than 47,000 people have been killed in nearly two decades of violence involving Indian troops and separatists in Kashmir.
The separatists put the toll at 100,000.