More than 80 people were killed, at least 50 of them in Sikkim.
Some 6,000 troops have been deployed in the north-eastern state to dig through mudslides and clear away rubble in an effort to reach cut-off villages.
Hundreds of people spent a second night in the open as aftershocks continued. The quake was felt elsewhere in India, as well as in Nepal, Tibet and Bhutan.
In the immediate aftermath of the quake heavy rains and landslides held up the relief effort. But a break in the poor weather meant that army helicopters were able to drop food supplies and transport medical teams to some affected areas.
Sikkim Chief Secretary Karma Gyatso told the BBC that rescue teams in the form of army personnel and a team of doctors had finally made it to the north of the state - the epicentre of the quake - where at least 33 people have died.
Mr Gyatso said that the number of dead was expected to "rise dramatically" because relief workers are yet to reach the inner parts of northern Sikkim where many people are feared to be trapped under debris.
"We have set up control rooms everywhere working alongside the army, the Indo Tibetan Police Force and the Sikkim police," Mr Gyatso said.
"We are trying to evacuate people stranded in inaccessible areas by helicopter, especially people in those areas where roads have been damaged."
Mr Gyatso said that with more than 100,000 homes in the state damaged, 2,500 relief camps had also been set up to provide people with some form of shelter.
Nevertheless, officials say the biggest challenge is reaching those villages in the most isolated areas of the mountainous state.
Convoys of vehicles left the state capital Gangtok on Tuesday morning but the AFP news agency says that progress was tortuously slow along precarious, badly-damaged roads.
SIKKIM: INDIA'S SECLUDED STATE
- Became part of India in 1975
- Has a population of 500,000 people
- Renowned for its spectacular mountains and lakes
- Economy largely dependent on tourism
On Tuesday, a break in the weather meant that helicopters were able to drop food and medical teams while evacuating some of the injured.
The earthquake triggered numerous landslides which crushed homes and blocked roads.
But troops and road workers managed to restore the main highway linking Sikkim with the rest of India.
But in the north of the state the situation remains uncertain.
"I've been here for six hours, waiting for the army to clear the road," Pema Doma, who was waiting for news of her parents and son in the Mangan area, told AFP.
"I'd walk if they would let me," Doma said. "The anxiety is killing me. What if he's screaming for me? What if he's calling for me and I can't even hear him?"
Similar efforts were under way in Tibet and Nepal where homes have been destroyed as well.
The magnitude 6.9 quake struck the mountainous state of Sikkim at 18:10 (12:40 GMT) on Sunday, according to the US Geological Survey, and was followed by two strong aftershocks.
Several earthquakes hit the Himalayan region this year, but none caused major damage.
Just over the border in Tibet's Yadong County, just 40km (25 miles) from Sikkim, the earthquake caused hundreds of landslides, disrupting traffic, telecommunications, power and water supplies.
China's official Xinhua news agency said that seven people had died and 24 others had been injured in Tibet. Landslides have also disrupted power and water supplies.
Nepal's government said 11 people had died, including two men and a child who were killed when a wall of the British embassy collapsed in the capital, Kathmandu.