Mobile services and internet remained suspended for the 16th consecutive day in the Valley.
Barricades around the Clock Tower in Srinagar's city centre Lal Chowk were removed after 15 days on Tuesday, allowing the movement of people and traffic in the commercial hub, as restrictions eased in several localities while continuing in others.
No students showed up in most primary schools that reopened on Monday but attendance in government offices has improved, officials said.
There was increased traffic flow in some parts of the Civil Lines areas of the city but curbs on movement persisted in Downtown Srinagar and in many parts of the Kashmir Valley, officials said.
Though restrictions were lifted in several places, the deployment of security forces continued to ensure law and order, they said.
A lot of private cars were seen plying in Dalgate, Boulevard, Sonwar, MA Road, Rajbagh and adjoining areas. Some inter-district cabs also plied in the morning, they said.
Markets in the Valley were shut, while public transport remained off the roads.
Mobile services and internet remained suspended for the 16th consecutive day, while landline telephone services in most areas also remained affected.
The authorities had said they would be restored across the Valley, except in a few vulnerable areas, by Monday.
Officials said the situation has remained largely peaceful since the Centre announced the abrogation of Article 370 and the reorganisation of Jammu and Kashmir into two union territories on August 5.
There were clashes between groups of youngsters and security forces in several parts of the Valley but authorities said the situation remained peaceful with few injuries reported.
Restrictions in many areas of Kashmir are being eased gradually since Saturday -- first for six hours in 35 police stations across the Valley and then for eight hours in 50 police station areas.
On Monday, the authorities made all necessary arrangements for the reopening of primary schools in the Valley, including 190 in the city. However, there were no students in most schools, particularly private educational institutions.
The civil secretariat - the seat of the Jammu and Kashmir government here - witnessed about 98 per cent attendance on Monday, while attendance in other government offices is improving, the officials said.