Authorities have imposed a curfew in Muslim-majority Kashmir for 11 days, blocked mobile phones and briefly ordered curbs on newspapers to stop people from gathering and to control the worst outbreak of violence there in six years.
Late Monday, protesters blocked a main road and threw stones at an army convoy.
"Some miscreants then tried to snatch weapons from the army and tried to set vehicles on fire," a police spokesman said Tuesday, according to Reuters.
The army opened fire after the protesters refused to heed warnings and two women were killed, the spokesman said.
A third person died in hospital Tuesday, taking the death toll to 42 since protests erupted over the killing of Burhan Wani, a 22-year-commander of a militant group on July 9.
About 3,500 people have been hurt, many with eye injuries caused by pellets Indian forces have been firing from a non-lethal weapon. The injuries have fueled anger.
Kashmir is India's only Muslim-majority state and has been contentious since India and Pakistan were carved out of British-ruled India and declared independent in 1947.
Both sides rule the Himalayan region in part but claim it in full and India has long accused Pakistan of arming separatist militants battling Indian forces in its part of Kashmir. Pakistan denies that.
The young separatist militant Wani represented a new generation of fighters in a region where alienation runs deep even though militant attacks have fallen dramatically since the revolt broke out in 1989.
India's interior minister, Rajnath Singh, said he had ordered security forces to exercise restraint. He told parliament he would visit Kashmir soon and hold talks with people "whose pain is being felt by every Indian".
The ruling Bharatiya Janata Party, which has long advocated a tough stand on Kashmir, shares power with a regional party in Kashmir and has been criticized for failing to address grievances.
Militants have called on social media for people in Kashmir to attack Indian forces, US intelligence group SITE said Monday.
The call was made by "brothers close" to Al Qaeda in the Indian Subcontinent and urged protesters to use petrol bombs, knives and iron rods, SITE said. Separatist groups have called for protests after prayers this Friday. Residents said they were running out of cash as banks were shut because of the curfew.