Mobile internet and social media remain largely blocked in Indian-administered Kashmir, despite a partial easing of curbs imposed when the government revoked its special status in August.
Limited broadband service returned to the Muslim-majority Kashmir Valley, while 2G mobile coverage resumed in parts of Hindu-majority Jammu.
Internet services were suspended across the region on 4 August.
India said the move was necessary to maintain law and order.
The Kashmir valley is the site of a long-running insurgency against Indian rule. A security crackdown and restrictions on communications were among measures imposed as India revoked the region's semi-autonomous status and split it into two federally-administered territories.
The government said the internet could be used to spread disinformation and allow militant groups to plan attacks.
But critics called the shutdown - the longest ever in any democracy - undemocratic and draconian.
The chief US diplomat for South Asia affairs, Alice Wells, is among those who have expressed concern.
"We remain concerned by detention of political leaders and residents, and internet restrictions. We look forward to a return to normalcy," she tweeted on Saturday, days after India arranged a tour of the region for some diplomats.
The communications blackout, which also initially included phone services, has badly hit the region's economy. Many businesses are struggling to operate.
The government's move restores a handful of broadband connections to "institutions dealing with essential services" such as banks, hospitals and government offices and these will be heavily monitored.
A government notice explicitly stated that access to social media sites or "peer-to-peer" messaging services like WhatsApp would not be restored.
Furthermore, internet service providers will be expected to install firewalls to prevent access to sites other than specific "white-listed" ones such as government websites.
In five districts in Jammu region 2G mobile connectivity was restored. The authorities restored broadband internet in Jammu last year, The Hindu reports.
India's Supreme Court last week ordered a review of the communications restrictions in place in Kashmir.
This, the court said, should be done within a week. "Suspension of free movement, internet and basic freedoms cannot be an arbitrary exercise of power," it said in its order.
Some mobile phone and landline services were restored in October, but the indefinite internet suspension has crippled daily life, the media and businesses.
The move in August by India's Hindu nationalist Bharatiya Janata Party (BJP) government to revoke the region's autonomy was controversial as the "special status" Kashmir enjoyed underpinned its fraught relationship with Delhi.