Afghanistan's fledgeling police force is a regular target of ambushes and roadside bombings.
Bashary said that the Taliban fighters had also suffered casualties, but he did not specify the number.
The Taliban said its men shot down the the Chinook in Helmand, the scene of a series of clashes between Taliban and Nato forces in recent months.
Major John Thomas, a spokesman for Nato in Afghanistan, admitted that the helicopter may have been shot down.
"It was a hostile area where the helicopter went down," he said. "And initial indications are that enemy fire may have brought down the helicopter."
|Afghan police convoys are a frequent target|
as the security force's presence expands
The 37-nation force does not release the nationalities of its casualties, but the ministry of defence said in London that one of the seven dead was a British soldier.
Qari Mohammad Yousuf, a Taliban spokesman, said 35 troops had been killed in the crash but Nato called that claim "absurd".
In an apparent response to the helicopter crash, dozens of suspected Taliban were killed in a joint Nato and Afghan raid in Sangin district, the Afghan defence ministry said.
"Tens of enemy elements have been killed and wounded," it said in a statement. "Various enemy locations were bombed by the air forces and the operation is still ongoing."