"A ceasefire is not going to do any good. We should not do anything to demoralise the security forces," said BJP spokesperson Sunil Sethi.
After an all-party meeting on Wednesday, Ms Mufti had said "all of us agree that we all have to appeal to the government of India to consider a ceasefire".
"The way Vajpayee ji announced unilateral ceasefire in 2000, the government of India should think on those lines," she had said.
But the BJP that shares power with Ms Mufti's party PDP made its disagreement public on a day the army chief told the Indian Express newspaper that "we will always fight those who seek azaadi, those who want to secede".
"No unilateral ceasefire was announced by then Prime Minister Atal Bihari Vajpayee in 2000. Only the Non Initiation of Combat Operation (NICO) by the army and security forces was enforced," the sources said.
The opposition National Conference is now attacking Ms Mufti, questioning the purpose of calling an all-party meeting when "her ally doesn't agree with her".
What was the point of @MehboobaMufti calling an all party meeting to build a consensus around initiatives in Kashmir when her ally in the Govt doesn't agree with her! Yet she will shamelessly cling to power because that's all that matters to her. https://t.co/HQ6P6yadPT— Omar Abdullah (@OmarAbdullah) May 10, 2018
The PDP insists there was consensus in the meeting that ceasefire was the way forward.
"Madam (Ms Mufti) said whatever we discussed there. That was the consensus. Let us see what happens next," said Basharat Bukhari, PDP leader and minister.