The clashes erupted as police fired tear gas to disperse thousands of people protesting the killing of the two by Indian forces in the southern Shopian area of the Indian portion of Kashmir, said senior paramilitary officer Nalin Prabhat.
As the news of the killings spread, thousands of people gathered in the towns of Shopian and Pulwama to take part in their funerals, chanting slogans in favor of Pakistan and against Indian rule.
Clashes erupted in Pulwama as police fired tear gas to stop the protesters from marching on the main road. The protesters responded by throwing rocks at the police and by burning an armored vehicle, police said, AP reported.
There were no reports of any injuries in the clashes.
Funerals for militants usually draw thousands in Kashmir, where sentiments against Indian rule run deep.
Rebels have been fighting since 1989 for Kashmir's independence or merger with Pakistan, which controls another portion of the territory in the west. More than 68,000 people have been killed in the militant uprising and Indian military crackdown.
India and Pakistan have fought two wars over control of Kashmir since they won independence from British colonialists in 1947.