Hekmatyar, a former prime minister whose forces operate in southeastern areas near Pakistan, denounced the US as "the mother of problems".
"As long as America remains in Afghanistan and in the region, war and problems will continue," he said in the video.
"I can say with full assurance and confidence that America does not have the ability to stay for a long period in Afghanistan.
"My analysis is that America [will] pull out from Iraq and Afghanistan simultaneously and the withdrawal perhaps will happen this year."
Hekmatyar said America's allies had sent troops to Afghanistan and Iraq out of fear of Washington, but he said a rift was emerging among them over whether they should stay on there.
Unlike other groups opposed to the US presence in Afghanistan, Hekmatyar has had an uneasy relationship with the Taliban and al-Qaeda.
His forces are believed to operate separately from the Taliban and operate mostly in the rugged southeastern areas bordering Pakistan.
Hekmatyar was Afghanistan's prime minister twice in the mid-1990s but he failed to agree with Ahmed Shah Massoud, his defence minister, and conflict between between the two eventually led to a prolonged and destructive civil war.
At one point he was supported by Iran's Shia government which has often been opposed to the staunchly Sunni Taliban which regarded Afghanistan's Shias as non-Muslims.
Hekmatyar was also the largest recipient of US and Pakistani aid in the 1980s during the Soviet occupation of Afghanistan.