At a meeting of top security officials that was also attended by the chief secretary and police chief of Jammu and Kashmir, National Security Advisor (NSA) Ajit Doval wanted the ceasefire proposal to come from separatists in the valley, according to sources.
After an all-party meeting in Srinagar last week, Ms Mufti had invoked former Prime Minister Atal Bihari Vajpayee and said "all of us agree that we have to appeal to the government of India to consider a ceasefire during Ramzan, Amarnath Yatra and Eid... the way Vajpayee ji announced a unilateral ceasefire in 2000".
"The idea should have come from separatists. They should have told terrorists to shun violence during Ramzan. Instead, she (Ms Mufti) announced it after the all-party meet when clearly not everyone was on board," a senior government officer told NDTV.
Ms Mufti's claim that there was consensus in the all-party meeting about a ceasefire has been contradicted by opposition parties like the National Conference and the Congress who say no such discussion took place at the meeting. The BJP that's part of the ruling coalition in the state has already snubbed the proposal, saying it will do no good.
Sources say the Prime Minister's Office is uncomfortable with the "unilateral ceasefire" usage by the chief minister. PM Modi is scheduled to visit Jammu and Kashmir on May 19.
"If the suggestion is to cease operations against terrorists, that's not going to happen until terrorists stop terrorist activities. Since Ramzan is a holy month for Muslims, terrorists should announce a unilateral ceasefire. If they stop killing civilians and attacking security forces, operations against them will automatically stop," said a senior officer at the Prime Minister's Office.
The month of Ramzan begins in a couple of days and the chief minister's proposal is yet to reach the central government.
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.