Authorities decided to re-open schools and colleges across the Kashmir Valley on Tuesday after shutting them the previous day to maintain law and order in the wake of a gunfight that killed three militants.

"All schools and colleges will re-open today (Tuesday) in the valley. Although the District Magistrates will decide if any educational institution needs to shut again for security concerns," officials said in Srinagar.

The separatists have also said that there would be no shutdown in the valley.

The educational institutions were ordered to shut down on Monday after the gunfight in Anantnag district.

One of the militant killed was Srinagar resident Essa Fazili, a B.Tech dropout from Baba Ghulam Shah Badshah University, Rajouri, who had joined militancy eight months ago.

While the Tehreek-ul-Mujahideen (TuM) outfit said Essa was a commander of their outfit, Islamic State (IS) flags were seen in funeral procession of the slain militant in Srinagar's Ahmed Nagar area on Monday evening.

In messages circulated on social media, IS affiliates have said that Fazili joined the ranks of the terror group's India branch, Ansar Ghazwatul Hind headed by local militant Zakir Musa.

Despite the claims, security forces including top intelligence officers have so far strongly refuted claims of IS presence in Jammu and Kashmir.