The group's spokesman, Zabihullah Mujahid, told media outlets that Taliban fighters had been advised not to attack members of any group, including the Kabul government, working to deliver aid to quake-stricken northeastern Afghanistan.
It was the second time this week that the insurgent group pledged to cooperate in relief efforts and showed support for victims of Monday's quake, which killed at least 115 people in Afghanistan and 272 in Pakistan.
The statements have come as a relief to Afghan officials because the Taliban has mounted major offensives against government forces across northern Afghanistan this year and controls portions of the remote province of Badakhshan, the quake's epicenter. The insurgent group reportedly captured Wardoj, the district next to the epicenter, on Oct. 2.
Immediately following the quake, some officials worried that insurgents would block aid efforts or attack government targets or international relief agencies as they have done in the past.
Wais Ahmad Barmak, director of Afghanistan's National Disaster Management Authority, suggested to lawmakers this week that the Taliban presence in several quake-affected areas was a hindrance to relief efforts. Afghan officials have not formally requested additional assistance, saying they are equipped to manage the response to the quake.
"We are faced with security problems in Kunar, Nuristan and Badakhshan provinces," Barmak told lawmakers on Wednesday.
Even without the Taliban presence, government authorities would struggle to reach the areas closest to the epicenter. Teams traveling on foot and donkeys have fanned out across the forbidding mountain region to report on the extent of damage. The Afghan government has not updated its casualty figures -- which include 583 people injured -- since Tuesday, seemingly due to a lack of information.
To those trying to deliver services in the most affected regions, the Taliban's statements were welcomed with relief.
"We have a very experienced medical team, but many of them are unwilling [or unable] to go to remote areas," said Ihsanullah Shinwari, director of the main hospital in the eastern province of Nangarhar.
The province, along the Pakistani border, includes districts where the Taliban has reportedly been battling with insurgents loyal to Islamic State. Shinwari said the security problems require patients to make long and often dangerous journeys to Jalalabad, the provincial capital, for treatment.
Nangarhar has reported 18 deaths from the quake, the second-highest number among Afghanistan's provinces after Kunar, where 31 people were killed. More than 400 houses were damaged in Nangarhar.
Most of the 82 patients admitted to the regional hospital following Monday's temblor were children from rural areas, he said.
Pakthun, a resident of Sorkh Rod district, a half-hour's drive west of Jalalabad, said he rushed to the side of his 2 1/2-year-old son, Adil, as soon as the tremors subsided. The boy was playing inside the house at the time of the quake.
"A wall fell on him," said Pakhtun, who has only one name. "It took 30 minutes for us to dig him out from under the rubble."
A few beds over from Adil lay 4-year-old Abdul Raziq, who was playing in the yard when he was pinned beneath the rubble of a collapsed wall.
"Several walls around the house started to fall one after the other," said his father, Abdul Hayat.
The boys were among the fortunate ones, able to reach medical services in time. UNICEF said children make up half the quake victims in Afghanistan and Pakistan.
Despite the initial panic, Shinwari said he is proud of how the hospital and community managed to treat the rush of patients.
"Doctors with private practices jumped into action and came immediately to the hospital to help," he said.
Special correspondent Arsalai reported from Jalalabad and Latifi from Kabul. Staff writer Shashank Bengali in Mumbai, India, contributed to this report.