At least 1124 people have died, 3251 have been injured and more than 8000 houses have been destroyed, said the Afghan Red Crescent Society, a humanitarian group working in the region, adding that more people are feared trapped under rubble.
The UN co-ordinator in Afghanistan said the toll was likely to rise.
Afghanistan is prone to deadly earthquakes, particularly in the Hindu Kush mountain range, where the Indian and Eurasian tectonic plates meet.
The earthquake, with a magnitude of 6,.0 struck about midnight on Monday at a shallow depth of 10km, with the eastern provinces of Kunar and Nangarhar being the worst hit.
Rescue operations were carried out in four badly hit villages in Kunar on Monday and efforts would now be focused on reaching more remote mountain areas, said Ehsanullah Ehsan, the provincial head of disaster management.
"We cannot accurately predict how many bodies might still be trapped under the rubble," Ehsan said on Tuesday.
"Our effort is to complete these operations as soon as possible and to begin distributing aid to the affected families."
Mountainous terrain and inclement weather have hindered rescuers reaching remote areas along the Pakistani border where the quake flattened hundreds of mud-and-brick homes.
Access for vehicles along narrow mountain roads was the main obstacle, Ehsan said, adding machinery was being brought in to clear roads of debris.
On Tuesday, a line of ambulances was on the damaged mountain road trying to reach Kunar villages, as helicopters flew in, bringing aid supplies and taking the injured to hospitals, according to a Reuters witness.
Thousands of children were at risk, the United Nations Children's Fund warned on Tuesday.
UNICEF said it was sending medicines, warm clothing, tents and tarpaulins for shelter, and hygiene items such as soap, detergent, towels, sanitary pads, and water buckets.
Taliban soldiers were deployed in the area, providing help and security.Â
The disaster has further stretched the war-torn nation's Taliban administration, already grappling with a sharp drop in foreign aid and deportations of hundreds of thousands of Afghans by neighbouring countries.
"Damaged roads, ongoing aftershocks, and remote locations of many villages severely impede the delivery of aid," the World Health Organisation said, adding that more than 12,000 people had been affected by the quake.
"The pre-earthquake fragility of the health system means local capacity is overwhelmed, creating total dependence on external actors."
The rescue and relief work has struggled in the face of tight resources in the war-torn, impoverished nation of 42 million people and limited global help in the aftermath of the tragedy.
So far, Britain has allocated Stg1 million ($A2 million) to support the efforts of UN and the International Red Cross in delivering critical healthcare and emergency supplies.
India delivered 1000 tents and was moving 15 tonnes of food supplies to Kunar, with more relief materials to be sent on Tuesday.
Other nations such as China, the United Arab Emirates, the European Union, Pakistan and Iran have pledged help but aid is yet to arrive.
Afghanistan has been badly hit by US President Donald Trump's decision in January to cut funding to its humanitarian arm USAID and reductions in other foreign aid programs.
Crises elsewhere in the world, along with donor frustration over the Taliban's policies towards women and curbs on aid workers have been a factor in funding cuts, according to diplomats and aid officials.
