General Mohammad Zahir Azimi, a defence ministry spokesman, denied the Taliban claim, saying there had been no "insurgent" activity in the area of the crash.
The M-17 helicopter was on its way from the western province of Herat to the neighbouring province of Farah when it went down.
Sayar was one of the Afghan army's four regional commanders and was in charge of Afghanistan's western region.
A recovery team had been sent to locate the crash site and retrieve the bodies and an investigation had been launched, Abdul Rashid, the district chief of Adraskan, said.
Two British soldiers serving with Nato-led international troops were also killed in an explosion while fighting Taliban in southern Afghanistan, military officials said on Thursday.
The blast occurred northeast of Gereshk district in the southern province of Helmand, the British defence ministry said in a website statement.
The fatalities brought to 141 the total number of British deaths in Afghanistan since their deployment in late 2001.