In the video statement, Hekmatyar also said he lost 10 men in the battle in Sarobi, the independent Pajhwok Afghan News agency reported.
The insurgent Taliban movement, which has unclear links with Hekmatyar's faction, has also claimed responsibility for the attack, which was the deadliest for the French military in 25 years.
Pajhwok told AFP the video was delivered to its office in Peshawar in Pakistan on Sunday.
He warns of "more guerrilla assaults on US forces besides the French soldiers," the agency said in a report on its website. The mountain ambush in Sarobi, east of Kabul, was the deadliest ground attack on international troops since they were sent to Afghanistan in 2001 to oust the hardline Taliban regime.
The attack, in which 21 troops were also wounded, shocked France and sparked debate about the country's involvement in war-torn Afghanistan.
But France announced last week it would beef up its mission in Afghanistan with helicopters, drones and other military means.
French officers have said the ambushed soldiers were confronted by about 170 heavily armed rebels who were better organised than usual.
They said they killed between 40 and 70 enemy fighters, but acknowledged they only recovered one body from the battlefield as they withdrew under the cover of darkness.
French authorities have denied a report in Canada's Globe and Mail newspaper that its soldiers were no match for the better-equipped and trained fighters who attacked them on August 18.
The Taliban, who were in government between 1996 and 2001, had immediately claimed the attack.
However, the extremists generally operate in southern and southeastern Afghanistan, while the areas around Kabul and in northeastern Afghanistan are said to be the domain of Hekmatyar.
The Taliban had previously rejected working with Hekmatyar's faction, but analysts have suggested they could be involved in some joint activities.
Hekmatyar, who served as prime minister briefly during the 1996 to 2001 civil war, is known as one of the most radical warlords in Afghanistan. The United States has offered a multi-million-dollar reward for his capture.