Three army officers, a senior police officer and three other soldiers were wounded in the operation, which follows the suicide attack last Thursday on a paramilitary convoy that killed at least 40 soldiers, the worst attack against Indian government forces in Kashmir's history.
India blamed the attack on Pakistan and promised a "jaw-breaking response." Pakistan has warned India against linking it to the attack without an investigation, saying that it was part of New Delhi's "known rhetoric and tactics" to divert global attention from human rights violations in Kashmir.
India and Pakistan each administer part of Kashmir, but both claim the Muslim-majority region in its entirety. The attack has led to a spike in communal tensions in Hindu-majority India. Videos of anti-Kashmiri protests have gone viral on social media, including some in which Kashmiri students were beaten by mobs of Hindu nationalist groups and warned to leave colleges and universities.
On the outskirts of the northern city of Ambala, about 300 Kashmiri students were forced to leave their rented accommodations by local Hindu residents, at least three students reached by phone told The Associated Press.
One of the students who asked to be identified by only his middle name, Ahmed, due to fear of reprisals from his university, said he and his fellow students felt unsafe despite police security. The Kashmiri students blamed Prime Minister Narendra Modi's Hindu nationalist ruling party for stoking anti-Muslim and anti-Kashmiri sentiment in India ahead of a general election due this year.
In another northern city, Dehradun, at least 20 Kashmiri students were forced to lock themselves in their hostel rooms for safety until police arrived, The Times of India newspaper reported. Police in Dehradun said the students were safe but refused to comment further.
Vijay Kumar, a top government adviser, said they received several complaints from students and businesspeople, and authorities were "doing everything possible for the security" of Kashmiris. He said authorities have spoken with officials in various cities and also set up help centers for Kashmiris living outside the state.
Reports of harassment elsewhere in India have triggered public anger in Kashmir, where authorities have suspended internet service on mobile phones and slowed other internet sources to try to stop the spread of videos or the organization of protests.
The Indian chapter of Amnesty International urged India's federal and state governments to "ensure that ordinary Kashmiri women and men do not face targeted attacks, harassment and arbitrary arrests" following Thursday's suicide bombing.
"We are at a dangerous moment, and authorities must do everything they can to uphold the rule of law," said Aakar Patel, head of Amnesty International India. "Ordinary Kashmiris across India who are only seeking to improve their lives should not be singled out for violence simply because of where they come from."
The statement said many students are reported to have fled their universities in fear. "Two colleges in Dehradun and one in Moradabad have stated that they will not admit new Kashmiri students," it said.
Monday's fighting in Kashmir triggered anti-India protests and clashes, with local residents, mainly youths, trying to march to the site of the gunbattle in solidarity with the rebels. Government forces fired tear gas at the stone-throwing protesters. No one was immediately reported injured in the clashes.
Residents said troops destroyed five civilian houses with explosives and gasoline during the fighting. Police said they recovered the bodies of the dead militants from the debris. A civilian was also killed in the crossfire, police said.
The dead soldiers included an Indian army major. Police said two militants were killed in the initial fighting, which resumed after a lull of about four hours, leading to the killing of a third militant and injuries to several soldiers and a police officer.
Rebels have been fighting Indian control in Kashmir since 1989 and the uprising and ensuing crackdown have killed about 70,000 people. Most Kashmiris support the rebels' demand that the territory be united either under Pakistani rule or as an independent country, while also participating in civilian street protests against Indian control.