A lockdown remains largely in place in the Muslim-majority Kashmir valley but authorities said they were re-opening nearly 200 primary schools in Srinagar, the largest city.
However, classrooms at schools visited by reporters mostly appeared empty. Parents said that they were worried about safety.
Despite the security clampdown in Kashmir, there have been frequent protests against the loss of special status and some have turned violent.
Kashmir is a Himalayan territory disputed by India and Pakistan. Each country controls part of the territory and the Indian-administered side – Jammu and Kashmir – has now been downgraded from a federal state and split into two union territories ruled by Delhi.
There has been a separatist insurgency in Jammu and Kashmir for three decades, with tens of thousands of people killed.
The government began partially restoring landline connectivity over the weekend, but mobile networks and the internet remained switched off as more protests were reported.
BBC correspondents report that many parents prefer to keep their children at home until mobile networks are restored.
The Reuters news agency quoted a teacher at one school as saying that students could not be expected to attend in such “volatile” conditions.
It added that a number of the schools supposed to open had been been locked or very lightly staffed.
Only government schools have re-opened, with private schools remaining closed, India’s PTI news agency reports.
Officials said that they were trying to ascertain how many students had attended in total.
The communications blackout in the region has made reporting from Indian-administered Kashmir difficult.
Prime Minister Narendra Modi has consistently defended the unilateral move to strip the region of its constitutional special status, saying that it was needed to facilitate economic development and improve security.
But Kashmiri political leaders and activists have characterised the decision as a betrayal and have voiced fury that it was implemented without any consultation with local leaders.
Well-known political leaders have been held in detention since the revocation of special status.