Many people spent a second night in the open after the 6.8 magnitude quake hit late on Friday. Relief workers face the challenge of reaching the most badly affected villages in the High Atlas, a rugged mountain range where settlements are often remote and where many houses crumbled.
Large chunks of a cliff had broken off and fallen on to the road near the small town of Moulay Brahim, partly blocking a winding road connecting Marrakech to the Atlas Mountains.
The latest Interior Ministry figures put the death toll at 2,012, with 2,059 people injured, including 1,404 in critical condition.
Morocco has declared three days of mourning and King Mohammed VI called for prayers for the dead to be held at mosques across the country on Sunday.
The World Health Organization said more than 300,000 people have been affected by the disaster.
"The next 24 to 48 hours will be critical in terms of saving lives," Caroline Holt, global director of operations for the International Federation of Red Cross and Red Crescent Societies, said in a statement.
Search and rescue efforts would be prioritised alongside making sure survivors were taken care of, she said, noting the importance of providing safe drinking water.
The village of Tansghart in the Ansi area, on the side of a valley where the road from Marrakech rises up into the High Atlas, was the worst hit of several visited by Reuters journalists on Saturday.
Its picturesque houses, clinging to a steep hillside, were cracked open by the shaking ground. Those still standing were missing chunks of wall or plaster. Two mosque minarets had fallen.
Abdellatif Ait Bella, a labourer, lay on the ground, barely able to move or speak, his head bandaged from wounds caused by falling debris.
"We have no house to take him to and have had no food since yesterday," said his wife Saida Bodchich, fearing for the future of their family of six with their sole breadwinner so badly hurt. "We can rely on nobody but God."
The village is already mourning 10 deaths including two teenage girls, a resident said.
PULLING SURVIVORS FROM RUBBLE
There were hopes more survivors could be found.
Footage captured on Saturday in the town of Moulay Brahim, some 50 km (30 miles) south of Marrakech, showed rescuers pulling someone from the rubble. Two rescuers hugged each other as the person was carried away on a stretcher.
The quake's epicentre was some 72 km (45 miles) southwest of Marrakech, a city beloved of Moroccans and foreign tourists for its medieval mosques, palaces and seminaries richly adorned with vivid mosaic tiling amid a labyrinth of rose-hued alleyways.
Marrakech's old quarter suffered extensive damage. Families huddled into the early hours of Sunday, spending a second night on the streets, fearing their homes were no longer safe to return to.
"I cannot sleep there. I am asking the authorities to help me and bring in an expert to assess whether it is possible for me to return to the house or not," said Mouhamad Ayat Elhaj, 51, on the streets with his family near the old city. "If there is a risk, I will not return to the house," he said.
It was Morocco's deadliest earthquake since 1960 when a quake was estimated to have killed at least 12,000 people, according to the U.S. Geological Survey.
Turkey, where powerful earthquakes in February killed more than 50,000 people, was among nations expressing solidarity and offering to provide support.
Marrakech is due to host the annual meetings of the International Monetary Fund and World Bank from Oct. 9.
An IMF spokesperson, asked about the planned meetings, said: “Our sole focus at this time is on the people of Morocco and the authorities who are dealing with this tragedy.”
