Ms Mufti's meeting with PM Modi revolves around Article 35-A - which bars outsiders from owning property in Jammu and Kashmir - being challenged in the Supreme Court.
A petition says the article discriminates against women of the state, who lose their right to own property in the state if they marry a "non-resident".
The article is considered fundamental to the special status of Jammu and Kashmir. Ms Mufti has said that if it is tinkered with then it will have a direct impact on demography of the state.
The Supreme Court has also asked the Centre to respond to another petition that challenges the validity of Article 370 of the Constitution, which grants Jammu and Kashmir its autonomous status.
"I told the PM that Jammu and Kashmir is going through a tough phase. People fear their identity is under threat...The message should go that Jammu and Kashmir is the pride of India, the taj (crown) of India and its special status should remain," Ms Mufti said.
The idea of India, she added, has to accommodate the idea of Jammu and Kashmir.
The Chief Minister's anxiety is linked to the opposite view of the ruling BJP, her alliance partner in the state. The BJP has long held the stand that Article 35-A is discriminatory in nature and should be scrapped. Yesterday, the BJP spokesperson in the state said the "time has come for the people of Jammu and Kashmir to say goodbye to Article 370 and revoke Article 35 A."
Yesterday, Ms Mufti met Home Minister Rajnath Singh. Sources say the Chief Minister wanted to know what the centre's stand would be in the Supreme Court.
Ms Mufti was reportedly told that "it is a procedural issue... the Attorney General would present the legal aspects as they exist in the constitution."
After meeting the Prime Minister, Ms Mufti said he was "very positive and said the alliance of PDP and BJP will be respected."