In Indian Kashmir, at least 11 people, including 10 suspected Islamic militants, have been killed in separate incidents of violence.
Indian police say suspected Muslim militants lobbed a grenade at a security patrol, but it missed its target and hit a group of civilians in a busy market in Kashmir's summer capital, Srinagar. At least one person was killed and several others injured.
Indian troops on Thursday also said they killed at least 10 suspected militants in gun battles in Kashmir. Most of the encounters between the army and the militants took place in remote mountain areas.
New Delhi says it will continue its operations against Muslim militants fighting to separate Kashmir from India, while honoring a truce with Pakistan along the Kashmir border. The largest Islamic insurgency group in Kashmir, the Hizb-ul-Mujahideen, also vows to carry on its struggle.
Despite the violence, the guns along the border have been silent since midnight Tuesday, giving border villages a second day of respite from the daily shelling.
India's former foreign secretary, Jyotendra Nath Dixit, says the cease-fire could be a step toward opening a dialogue between New Delhi and Islamabad.
"It is a positive step, and maybe it is a tentative beginning move toward some kind of normal interaction leading to a political dialogue," he said.
India insists it will only open negotiations with Pakistan when it stops allowing armed militants to cross the border into Indian Kashmir. Pakistan denies permitting militants to move across from its territory.
But Indian officials are sounding more optimistic since the truce has been announced. Foreign Minister Yashwant Sinha told India's Hindu newspaper that the cease-fire has improved the climate for peace. He also said New Delhi would respond positively to what he called any "worthwhile suggestion" from Islamabad.
On Thursday, Islamabad's foreign ministry spokesman, Massod Khan, called it a "good beginning."
The ceasefire is the most significant peace move between the two countries since they began to mend their ties earlier this year.
The Kashmir region, divided between India and Pakistan, has long been a sore point between the two nations, and the trigger of two of their three wars.