He urged Khattar to meet the family as it would instill a sense of confidence in them, and also ensure a prompt and impartial probe into the "most brutal" incident.
An official release said Khattar assured Kumar that he would meet the boy's family members and ensure a fast and impartial investigation.
The family originally hails from the Madhubani district of Bihar.
"I talked to the mother and the uncle of the victim this morning to express my heartfelt grief over the incident. And after talking to them, I had a telephonic conversation with Haryana CM Manohar Lal Khattar," Kumar told reporters.
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"During my telephonic conversation, the Haryana CM ensured that the culprit responsible for the child's murder would not be spared," he told reporters after his weekly 'Loksamvad' programme.
The class-2 student of the Ryan International School was found murdered with his throat slit in a washroom of the school last Friday.
Kumar described it as "most brutal" incident which has shocked the entire nation and sent an alert to force all schools- government as well as private ones - to follow security norms.
Kumar had asked Khattar yesterday also to take stern action against those involved in the killing. He had also spoken with the father of the boy.
The Bihar CM had directed the Resident Commissioner in Delhi to immediately send officials to Gurugram to meet the grieving family and console them.
On his directives, Bihar Director General of Police P K Thakur had talked to his Haryana counterpart and requested him to to take strong action against the culprits.