Two Indian soldiers and one civilian were killed in another gun battle in Kachdoora village, which is also in Shopian district, where a battle with a separate group of 4-5 militants was ongoing, Vaid said.
The use of pellet guns is controversial in Kashmir.
Earlier opposition Awami Itehad Party (AIP) leader and lawmaker Engineer Sheikh Abdur Rashid also along with his party activists held a protest against Sunday's incidents.
Over 100 people were injured in the clashes.More news: Spring storm packing heavy snow
In Occupied Kashmir, complete shutdown marked by curfew and restrictions is being observed against the killing of 17 youth by Indian troops in the held territory.
In retaliatory firing by security forces, four civilians were killed and over 50 others were wounded.
A large majority of civilians in Kashmir - India's only Muslim-majority state - support the freedom fighters who have been fighting for decades for independence or for a merger with Pakistan. They also stopped train services and cut cell-phone internet services in the most restive towns, and reduced connection speeds in other parts of the Kashmir Valley, a common government practice aimed to calm tensions and prevent anti-India demonstrations from being organized.
In 2016, Srinagar's main hospital alone received hundreds of patients who had been injured in their eyes and blinded by shotgun pellets after some of the biggest protests against Indian rule in response to the killing of a charismatic young rebel leader, Burhan Wani.
Pakistan, it said, expresses its full solidarity with Kashmiris and "we urge global community to take cognisance of the gross and systematic violations of fundamental human rights".More news: Sister Jean Left the Court Before Loyola-Chicago's Final Four Loss Ended
"I will like to make it clear that our operations against militants will not stop", IG CRPF Zulfiqar Hassan told reporters while addressing a joint press conference with GoC 15 Corps Lt Gen AK Bhatt and DGP Vaid, said media reports.
As the fighting raged, anti-India protests erupted in several villages in southern Kashmir.
Anti-India sentiment runs deep in Kashmir, which in recent years has seen renewed rebel attacks and repeated public protests against Indian rule.
Tens of thousands of people have been killed in the conflict in Kashmir, which nuclear-armed India and Pakistan claim in full.
Most of Indian-controlled Kashmir was shuttered on Monday due to the Indian army's clampdown and the pubic strike.More news: US Open champion Stephens wins Miami Open title