Major John Thomas, and IAF spokesman, said: "The helicopter burst into flames ... It seems that no one on board could have survived."
Small crew
The CH-47 Chinook, a heavy transport helicopter with two rotors, can carry up to around 40 troops plus a small crew.
The fact it was flying at night suggests the helicopter may have been carrying troops on a night-time air assault.
A British military spokesman in Helmand, where most of the group of about 5,200 British troops with ISAF is based, said there had been "an incident involving some casualties" but would give no details.
He said: "The foreign troops have cordoned the area and are in control of the crash site so we cannot have access to the area to determine the number of casualties."
Taliban claim
Ahmadi, who regularly speaks to the media from an undisclosed location on behalf of the Taliban, said he had received the information from Taliban in Helmand.
He said he did not yet know exactly how the aircraft had been brought down.
Ahmadi said Taliban fighters have anti-aircraft weapons dating from the period of resistance to the Soviet occupation of the 1980s, but also that "they have received new anti-airplane weapons".
He said: "At this stage I don't have the exact information which weapons they used to bring down the aircraft."
US assessment
Earlier in the day, a senior US military officer said Western forces in Afghanistan had the Taliban on the defensive after a series of spring battles that had also been blamed for a rising civilian death toll.
"We think that we have got the Taliban on their heels," said Brigadier-General Perry Wiggins, deputy director for regional operations in the Joint chiefs of staff, a group which brings together the chiefs of all the branches of the US military.
Wiggins told a news briefing at the Pentagon that several senior Taliban leaders had been killed in clashes which had forced the anti-government group to further pursue smaller-scale "asymmetric" attacks such as suicide bombings.
He said: "Although it has not crippled them, it'll set them back for a period of time."