SRINAGAR, Indian-controlled Kashmir (CNN) -- Two soldiers, including an officer, and three militants have been killed in a fierce gunfight in the Kupwara district on the north Kashmir frontier, the Indian army said Monday.
Indian paramilitary forces stand guard as a curfew goes into effect in Srinagar on Monday.
An army spokesman said the gunfight erupted Saturday during a search operation in the forested area of Hatmulla, near the Line of Control that marks the border between India and Pakistan in Kashmir.
"The search party of the army was fired upon by holed-up militants, resulting in the death of an army major and a trooper," Lt. Col. J.S. Brar said. "In the resultant encounter, the troops gunned down three terrorists."
Searches continue in the area, he said.
Separately, four people were injured by Indian security forces Monday as they and other protesters tried to march into the town of Shopian in south Kashmir, where claims of the rape and murder of two women on May 30 touched off a week of protests.
Separatist have called for a total shutdown of the region because of the deaths, crippling life across Indian-administered Kashmir for eight days, with shops and businesses closed and traffic off the roads.
According to a senior police officer, a case of rape was registered in the local police station Sunday after the forensic science laboratory confirmed that the two women had been raped.
The shutdown and protests were called by hardline separatist leader Syed Ali Shah Geelani, who after remaining under house arrest for more than a week was whisked away Saturday evening from his residence for an unknown destination.
Indian authorities imposed curfew-like restrictions in the capital, Srinagar, on Monday morning and moved in additional heavy contingents of police and paramilitary to scuttle protests.
Indian police and paramilitary troops enforced strict restrictions, banning all forms of vehicular and pedestrian movement in the city. Major intersections were barricaded with razor-fitted wire.
Shopian, 60 kilometers (more than 35 miles) from Srinagar, also was sealed by security forces.
Those forces fired on an emotional crowd of protesters Monday afternoon as they tried to march into Shopian. Four people were taken to a hospital with gunshot wounds.
Geelani had called for people from throughout Kashmir to march to Shopian on Monday.
In the protests of the past week, a youth was killed and more than 300 people were injured in the clashes with security forces.
Protesters are demanding that the "guilty be punished" in the deaths of Asiya Jan, 17, and her sister-in-law Neelofar Jan, 22, whose bodies were found May 30 by the side of a stream in Shopian. Relatives and local villagers allege that the two were raped and murdered by Indian security forces, a charge strongly denied by authorities.
Under pressure from the public and the opposition pro-India Peoples Democratic Party, the state government announced a judicial investigation, which will be headed by a retired high court judge.