At least 61 people, mostly stone-throwing protesters, have been killed over the past two months, when Kashmir has seen the largest pro-independence demonstrations in two years.
The killings of civilians have fuelled anger in disputed Kashmir, a region where sentiments against New Delhi's rule run deep but militants violence is waning.
"Police opened fire after violent demonstrators attacked a police station Bijbihara. One person died and several others were injured," a police statement said.
Bijbihara town lies in south Kashmir while another protester was shot dead when clashes broke out in north Kashmir, police said.
The fresh deaths brought thousands of people out in streets across the valley shouting "we want freedom."
An over two-month-long separatist strike and security lockdown has kept the Kashmir Valley on the boil, shutting down much of a region where tens of thousands of people have been killed since an insurgency broke out in 1989.
Peace in Kashmir is seen as crucial for improving relations between New Delhi and Islamabad, who are trying to revive peace talks that were halted after India blamed Pakistan-based militants for the 2008 Mumbai attacks.
