There were no signs so far that the plane had been brought down by enemy activity, the source said, and there were believed to be fewer than 10 people on board.
A spokesman for US forces in Afghanistan, colonel Sonny Leggett, said that the Bombardier E-11A crashed in the Ghazni province and an investigation is ongoing.
However, the insurgent group claims that it killed “lots” of people when it downed the aeroplane, including high-ranking officers.
Taliban spokesman Zabihullah Mujahid said: “The plane, which was on an intelligence mission, was brought down in Sado Khel area of Deh Yak district of Ghazni province.”
“Lots” of US service members were killed, Mr Mujahid said.
Tariq Ghazniwal, a journalist in the area described as having links to the militants, posted video to Twitter of what he claimed was the downed plane.
He said he saw two bodies on the ground and the burning aircraft around six miles (10km) from a US military base.
His information could not be independently verified, the Press Association said.
Earlier, Major Beth Riordan, a spokeswoman for US Central Command, confirmed army officials are investigating reports a military plane crashed in a Taliban-held area but said at that point it was not clear whose aircraft was involved.
And there were reports earlier that a passenger plane from Afghanistan’s Ariana Airlines had crashed in the eastern Ghazni province, a mountainous area controlled by the Taliban.
However, the state-run carrier said none of its planes had crashed in the country.
The video shows the remains of what could have been a Bombardier E-11A plane, used for surveillance and nicknamed “wi-fi in the sky”.
The plane went down at around 1pm local time (8.40am GMT) in Deh Yak district, some 80 miles (130km) southwest of the capital Kabul, according to Arif Noori, spokesman for the provincial governor.
Two provincial council members also confirmed the crash.
Mr Noor said it happened in territory controlled by the Taliban, which currently rules around half of the country.
The Pentagon has declined to comment.
