Mr Chidambaram said the "muscular and militaristic" approach of the Modi government has driven the state towards a "catastrophic" situation.
"Mehbooba Mufti should break her party's unholy and opportunistic coalition with the BJP and go back to the philosophy of her father," Mr Chidambaram tweeted.
Ms Mufti, 58, succeeded her father Mufti Mohammad Saeed who died in January 2016, as chief of the People's Democratic Party or PDP.
"The PDP-BJP coalition is the gravest provocation to the people of the Kashmir valley. Mehboobaji, quit the coalition immediately and go back to the people," the former union finance minister tweeted.
On Monday, Ms Mufti had called for ending the cycle of violence that has consumed the state. Five Hizbul Mujahideen terrorists were shot dead in Shopian on Sunday, and five civilians were killed in the clashes that followed the encounter. A tourist from Chennai, who was attacked by stone-throwers near Srinagar, also died in hospital on Monday night.
The central government's muscular, militaristic approach to the J&K issue has driven the State towards the present catastrophic situation.- P. Chidambaram (@PChidambaram_IN) May 8, 2018
Mr Chidambaram said he shared Ms Mufti's concern that statesmanship is needed to get the state out of the cycle of killings.
The first four months this year saw 100 deaths, including 55 terrorists, 20 security personnel and 25 civilians. Of the 55 terrorists killed, 27 were locals.
On a question about home-grown terrorism and more Kashmiri boys joining terror groups, Director General of Jammu and Kashmir Police SP Vaid said, "Obviously, it is a big concern for us and we will take steps to deal with it."
With inputs from PTI
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