United States National Security Advisor Susan Rice in her phonecall to her Indian counterpart said the White House expects Pakistan to take "effective action to combat and delegitimise" United Nations-designated terrorist groups.
Naik Rajkishor Singh, died of his injuries on Friday.
Singh's comments came hours after a Border Security Force and adjoining army camps in Baramulla were attacked by heavily armed militants on Sunday night.
Not ruling out the violation of Standard Operating Procedures when such a huge movement of central forces is taking place in the troubled state, officials requesting anonymity said a clear picture on loopholes, if any, will be known after a thorough probe.
The United States has slapped sanctions on Pakistan-based terrorist leader Bahawal Khan for being involved in terrorist attacks in Afghanistan and Pakistan.
Modi visited the border district in Jammu region, his first to Jammu and Kashmir after the abrogation of Article 370, coinciding with Infantry Day celebrations.
The incident took place when the terrorists launched a 'fidayeen' (suicide) attack on 46 Rashtriya Rifles army camp in Baramulla district of north Kashmir. The camp is located on the outskirts of Baramulla city, 54 kilometre from Srinagar.
The officials said they had no information other than that Azhar was undergoing treatment at an army hospital after suffering renal failure.
Home Minister Rajnath Singh, Defence Minister Manohar Parrikar, Finance Minister Arun Jaitley, National Security Advisor Ajit Doval, Army Chief General Dalbir Singh Suhag besides other senior officials attended a meeting with Prime Minister Narendra Modi.
It is believed that the attack was the handiwork of a freshly-infiltrated group of terrorists who could have entered along the Salamabad Nallah into the town.
'Pakistan will try to escalate covert operations through terrorism,' says Dr Shalini Chawla.
'What Modisaab will accomplish by tampering with the treaty is providing ammunition to ultra-nationalist right wing elements within Pakistan who see India as an existential threat.'
Immediately after India launched its surgical strikes, sources said, it had informed the US of its action.