A curfew is in force in Shopian, a town at least 60km south of Srinagar, where one protester was killed and 19 people injured, including six police officers in clashes between security forces and protesters, according to doctors and police officials.
Mohammed Yousuf, a doctor in Shopian's main hospital, said seven of the injured were in critical condition.
A second protester was killed in Baramulla, a town north of Srinagar, when he was hit with a tear gas shell, said a local police officer who spoke on the condition of anonymity.
Mohammed Yasin Malik, a senior separatist leader and chief of the Jammu Kashmir Liberation Front (JKLF), was injured when police used teargas and batons to disperse thousands of demonstrators he was leading in Srinagar.
"Malik fell unconscious and was immediately removed to the hospital," Showkat Bakhshi, a JKLF spokesman, said.