Taliban government officials have urged aid organisations to aid the rescue effort in the remote mountainous areas.
The police chief of Kunar province tells the BBC toads to the area are blocked due to landslides caused by flooding and quake aftershocks.
He said rescue operations can only be carried out by air.
The Taliban officials say they have limited resources and are requesting help from international organisations to provide helicopters to reach affected areas.
Modelling suggests hundreds of possible deaths
The US Geological Survey (USGS), a governmental department which monitors earthquakes, suggests hundreds of people could be killed in this quake.
Modelling on its website estimates that "significant casualties are likely" as the disaster is potentially "widespread".
The USGS notes that previous earthquakes in the region at the same alert level have required a regional or national level response.
So far 20 people have been confirmed to be killed.
Whole villages are under rubbleBREAKING
Multiple sources from the Taliban government have told the BBC that “dozens of houses are under rubble” and it is now feared that hundreds of people could be killed and wounded in the earthquake.
It is believed that mostly houses are damaged in Mazar valley, in the Norgal district of Kunar province which shares a border with Pakistan.
The valley is located in a mountainous area.
So far 20 people have been confirmed killed in the quake.
A 6.0-magnitude earthquake hit Afghanistan’s eastern region near the Pakistan border on Sunday, according to the United States Geological Survey (USGS).
USGS reported that the quake occurred 27km (16.77 miles) north-east of Jalalabad, in Nangarhar Province, and at a depth of 8km (4.97 miles). It struck at 11:47 p.m. local time. USGS models estimate the shaking could result in hundreds of fatalities.
Nearly half a million people likely felt strong to very strong shaking, which can result in considerable damage to poorly built structures, according to the USGS.
At least nine people were killed and 25 others were injured in Nangarhar, Reuters reported, citing Ajmal Darwaish, spokesman for the province’s health department.
“Unfortunately, tonight’s earthquake has had human casualties and financial damages in some of our eastern provinces,” Taliban spokesman Zabihullah Mujahid posted on X.
“Right now, local officials and residents are making all the efforts to rescue affected ones. Support teams from the capital and nearby provinces are also on their way. All available resources will be used for the rescue and relief of the people,” he added.
Around 20 minutes after the quake struck, a 4.5-magnitude aftershock hit the same region, according to USGS, later followed by a 5.2-magnitude aftershock — both at a depth of 10km (6.21 miles).
An orange alert was issued by the USGS PAGER system, which predicts economic and human loss after earthquakes.
“Significant casualties are likely and the disaster is potentially widespread. Past events with this alert level have required a regional or national level response,” it said.
Ahmad Zameer, 41, a resident in Kabul, told CNN the earthquake was strong and jolted his neighborhood more than 100 miles from the epicenter. He added that everyone from the nearby apartment buildings rushed to the street in fear of being trapped inside.