James Bays, Al Jazeera's Afghanistan correspondent, said: "They [the Taliban] said the reason that they didn't go ahead with their threat [to kill the hostages] was that they have been contacted directly by the deputy interior minister of Afghanistan."
There had been uncertainty about the fate of the hostages for hours after the Taliban's "final" deadline passed at 20:30 GMT on Wednesday.
Bays also reported another Taliban source as saying the remaining hostages "have been split up into smaller groups".
The group has threatened to kill the remaing hostages, 22 fellow Christian volunteers, unless the Afghan authorities agree to demands to release Taliban prisoners in exchange for the hostages.
But the Afghan authorities have publically refused to swap prisoners for the hostages.
One hostage killed
On Wednesday, the Taliban killed one of the hostages. Afghan officials confirmed they had recovered the bullet-riddled body of Bae Hyung-Kyu, a Presbyterian pastor and the leader of the South Korean group.
The Taliban claimed responsibility for the killing, accusing the Afghan government and South Korean negotiators of failing to act in good faith after they rejected an initial list of eight Taliban fighters to be freed from prison.
"Since Kabul's administration did not listen to our demand and did not free our prisoners, the Taliban shot dead a male Korean hostage," a Taliban spokesman said.
South Korea has condemned the Taliban for the killing of Bae.
Baek Jong-chun, the chief national security adviser, said on Thursday: "The government and the people of South Korea condemn the kidnapping of innocent civilians and the atrocity of harming a human life."
"Harming innocent civilians can never be justified and we will never forgive this kind of inhumane act," he said in a nationally televised statement.
Bae, who was killed on his 42nd birthday, was co-founder of the Saem-Mul church which sent the volunteers to Afghanistan. He had a wife and nine-year-old daughter.