"The Taliban found and recovered four al-Qaida mujahidin this morning," the group's spokesman, Abdul Latif Hakimi, said on Thursday from an undisclosed location.
Hakimi, whose links to the Taliban are not clear, declined to say where the escapees were, but added: "They are far away from Kabul. They are safe and now taking rest."
The US military said it was pressing on with an "aggressive" hunt for the men, who broke out of the detention centre at Bagram Air Base, 50km north of Kabul on Monday, and declined to comment on the Taliban claim.
"The only comment I have is that the search is ongoing and we are investigating the circumstances of how they were able to escape," Lieutenant-Colonel Jerry O'Hara said.
The escape was the first known from the Bagram base and a major embarrassment for the US military, which has refused to identify the escapees except to say they were "dangerous enemy combatants".
The escape is seen as a major
embarrassment for US forces
But Afghan officials named the men as Syrian Abdullah Hashimi, Kuwaiti Mahmoud Ahmad Mohammad, Saudi Mahmoud Alfatahni and Libyan Mohammad Hassan.
The US military provided Afghan security forces with photographs of the escapees, which showed bearded men in orange prison uniforms whose ages appeared to range from 20 to 40.
A US spokesman said on Wednesday that it appeared the men had changed into less distinctive clothes to make their escape.
Meanwhile, a Taliban leader told Aljazeera on Thursday that the group's insurgents possessed anti-aircraft weapons and were seeking to obtain even more powerful arms.
"We cannot reveal our military secrets but, by the will of God, we will obtain weapons more powerful than what we have," Mullah Dadullah, a member of the Taliban's leadership council, told Aljazeera in an interview broadcast on Thursday.
The Taliban says it has weapons
that can bring down aircraft
"We have weapons that can down aircraft, but we cannot reveal what they are," he added without elaborating.
Last month, Taliban insurgents shot down a US helicopter, killing all 16 troops on board, in the biggest single combat blow to US forces since they overthrew the Taliban in 2001.
Taliban spokesman Hakimi had said the fighters shot down the helicopter with a "new type of weapon".
US military officials, however, had said the aircraft was probably shot down by a rocket-propelled grenade and there was no indication that a more sophisticated ground-to-air system was involved.