District magistrate Srinagar Farooq Ahmad Lone said there would be no restrictions in any area of Srinagar city on Sunday.
However, as a precautionary measure, restrictions will continue in Handwara and Kupwara towns on Sunday to maintain law and order, the authorities said.
Despite restrictions in parts of Srinagar city on Saturday, there was a perceptible improvement in the situation over the last three days as skeletal transport operated and some shops had opened for locals to buy essentials in civil lines and outskirts of the city.
District magistrate Kupwara Kumar Rajiv Rajan said restrictions would remain in force in Kupwara and Handwara towns on Sunday because of tension in the district.
Separatist leaders have also not called for any shutdown or protests on Sunday.
Parts of Srinagar city, including old city areas, remained under curfew-like restrictions during the last four days following killings of five civilians in firing by the security forces in Handwara, Drugmulla and Natnusa areas of Kupwara district.
Authorities have still not revoked the suspension of mobile internet services which have remained suspended in Kashmir valley for the last five days.
Jammu and Kashmir Chief Minister Mehbooba Mufti met the family members of killed youth during her visit to Kupwara district on Saturday.
Mufti met them at Kupwara Dak Banglow where she chaired a security meeting attended by Deputy Chief Minister Nirmal Singh, chief secretary B.R. Sharma and police chief K. Rajendra Kumar.
Mufti condoled the bereaved families and regretted that she had to come to Kupwara for offering condolences while she had planned to visit there as the chief minister to announce a special package for the border district.
The chief minister told relatives of the victims that anybody found guilty of having violated the SOP (standard operating procedure) during crowd control in recent incidents will have to face the law.
"I have spoken to the top officers of the army and told them civilian killings are not acceptable. Those found guilty of using excessive force against protesting civilians will be punished," she assured them.
She also ordered ex gratia relief and other compensations to the next of kin of those who lost lives in Kupwara district due to firing by security forces.
Meanwhile, the police late Saturday produced the minor girl allegedly molested by a soldier in Handwara on Tuesday before the chief judicial magistrate (CJM) under directions of the state high court.
The girl made a statement before the magistrate about the incident that triggered widespread violence in Handwara town on Tuesday.
The high court has directed the police to declare the provisions of law under which the minor girl was being detained.
This followed a petition filed by the girl's mother on Saturday. The next hearing of the case has been fixed for April 20.
Giving details of the law and order situation in Kashmir Valley during the past five days, S.J.M. Gilani, IGP (Kashmir), said over 200 policemen including three superintendent of police and two deputy superintendent of police have been injured during this period.
The inspector general of police said 28 civilians were injured during this period out of whom six were admitted in hospital and recuperating well from injuries sustained during the clashes.(IANS)