Unidentified gunmen killed a leader of India's ruling Hindu nationalist Bharatiya Janata Party (BJP) in Jammu and Kashmir state late on Thursday, prompting authorities to impose a curfew in the area.
Anil Parihar, 53, state secretary of the BJP, and his brother, Ajit, were shot dead in the predominantly Muslim town of Kishtwar, while they headed home after shutting their shop, police said.
Police are investigating whether it was a militant attack or a criminal act, a senior police officer said.
Anil Parihar was an influential leader in the region. He was considered a moderate and had a sizeable support base, even among Muslims, media reported.
Indian Kashmir, its only Muslim-majority state, has been beset by a 29-year-old insurgency.
India accuses Pakistan for sheltering anti-India militants but Pakistan denies that. Pakistan, which like India, claims the whole of Kashmir, calls for talks to decide the region's future.
The BJP leader in the state had two bodyguards but they were not with him at the time of the attack, said Kishtwar's senior police official, Rajinder Gupta.
Kashmir is under direct rule by the federal government, which gives the BJP a free hand to control it ahead of a general election that must be called early next year.
Federal home minister Rajnath Singh said he was shocked and pained by the killing of the brothers.
"Police will leave no stone unturned to bring the perpetrators to justice," Singh said on Twitter.
Kashmir has been at the heart of decades of hostility between India and Pakistan, which have gone to war over it twice since independence from Britain in 1947.