The two groups are battling for territory in the remote north of the country.
The Afghan government is offering to make the Taliban a political party.
The longest-serving commander in the longest war in U.S. history said he would welcome Moscow's help.
Insurgents such as the Taliban and ISIS exert more control or influence than ever previously recorded by a Congress-mandated watchdog.
“Don’t worry, those are people that are tied to me...They are Taliban."
"We know that the Russians are involved," claimed Gen. John Nicholson.
The extremist leader has been linked to a plot to attack Times Square in New York City.
Insurgents for the group overran three checkpoints in night raids on Tuesday.
The demand comes after two major Taliban attacks in Kabul that left 150 civilians dead.
Former Defense Secretary Chuck Hagel said the U.S. military “can’t fix the problems in Afghanistan” and Russia “really holds the cards” in Syria.
For the first time ever, the Pentagon blocked the release of territorial control data in the Afghanistan conflict, but a BBC study painted a grim picture.
The Pentagon told an independent watchdog not to publish numbers on insurgent control of Afghanistan, despite the fact that the data is unclassified.
Health ministry spokesman Wahid Majroh said at least 40 people were killed and 140 wounded in the blast.
"We have sacrificed a lot. We have paid a huge price both in blood and treasure," a spokesman said.
Archaeologists in their 80s have been coming out of retirement to help with this stunning development.
The military carried out large strikes against opium production hubs in northern Helmand on Sunday.
The couple wants Taliban leaders to be tried for war crimes after their release.
The Afghan government's control over the war-torn country has "deteriorated," but the U.S. refuses to show how badly local forces have suffered.
"There are, we believe, moderate voices among the Taliban," he said.
Coleman and her husband were captured by the Haqqani network almost five years ago.
The militant group says it would prefer that women learned how to use grenades.