An army major was among the dead, along with two militants from the Pakistan-based Jaish-e-Mohammed (JeM) group which claimed last week's attack, military and police officials said
Indian troops suffered new losses on Monday in a battle with Kashmir militants that left at least seven dead, officials said, just days after a major suicide bomb attack escalated tensions with neighbouring Pakistan.
The confrontation piled more pressure on the Indian government, which has blamed Pakistan for last Thursday's suicide attack on a convoy that killed at least 41 paramilitaries.
Several hours of shooting rocked the Pulwama district, south of Kashmir's main city of Srinagar, after officials reported that four soldiers, two militants and a civilian were killed in the latest clash.
An army major was among the dead, along with two militants from the Pakistan-based Jaish-e-Mohammed (JeM) group which claimed last week's attack, military and police officials said.
"The encounter is still on," Colonel Rakesh Kalia, a military spokesman in Kashmir, told AFP.
Hundreds of soldiers raided villages and fired warning shots at a suspected militant hideout, unleashing the firefight in the village of Pinglan.
Some militants were believed to have escaped, police said, and government forces cordoned off other villages as they gave chase.
Government forces have launched a massive hunt since an explosives-packed van struck the convoy transporting 2,500 security men close to Pinglan on Thursday.
A video on social media purportedly shows a pre-recorded message by the 20-year-old Kashmiri suicide bomber warning of more attacks.
Pakistan has denied any role in the attack.
As Islamabad recalled its envoy to New Delhi for "consultations", India's Prime Minister Narendra Modi on Monday called for greater international action against "terrorism".
"The cruel terrorist attack in Pulwana shows that time for talks is over," Modi told reporters after meeting with Argentina's President Mauricio Macri in New Delhi.
Thousands of demonstrators staged angry rallies in several Indian cities over the weekend, with attacks on Kashmiris reported in different towns.
Protesters in New Delhi on Sunday burned effigies of Pakistani and JeM leaders.
Many small businesses closed Monday following a call for a nationwide shutdown.
In the capital, a Kashmiri man was beaten by a mob that accused him of chanting anti-India slogans. He was later detained by police.
A curfew remained in force for a fourth day in Jammu city, in the Hindu-majority part of Kashmir, where mobs attacked and set fire to properties belonging to Kashmiri Muslims.
Thousands of residents in the city have fled to Muslim-majority areas.
The government faces increased pressure because of an upcoming national election.
New Delhi has withdrawn trade privileges for Pakistan and ended police protection for four Kashmiri separatist leaders.
Some commentators have called for military action against Pakistan however.
India launched what it called 'surgical strikes' on targets in Pakistani Kashmir in September 2016, 11 days after a militant attack on an Indian army base in Kashmir which left 19 soldiers dead. Pakistan denies the strikes took place.
But experts say India has limited options for action now.
"Whatever retaliation India takes will be symbolic. It won't have any real impact," Ajay Sahni, executive director of the New Delhi based Institute for Conflict Management, told AFP.
Saudi Foreign Minister Adel al-Jubeir said during a visit to Islamabad that his country "will try to de-escalate tensions" between India and Pakistan. He is due to visit New Delhi with Crown Prince Mohammed bin Salman on Tuesday.
JeM is one of several militant groups fighting Indian troops in Kashmir, which has been split between India and Pakistan since independence from Britain in 1947. Both claim the Himalayan region and have fought two wars over the territory.
Kashmir is the world's most militarised zone with some 500,000 Indian troops deployed to fight a rebellion that broke out in 1989.
Tens of thousands of people, mainly civilians, have died in the conflict. Violence has spiked since 2016 with almost 600 killed last year, the highest toll in a decade.