Everyone aboard -- six U.S. Air Force members and five civilians -- died in the incident, the U.S. military said.
The Pentagon on Saturday identified the airmen as Capt. Jonathan J. Golden, 33, of Camarillo, California; Capt. Jordan B. Pierson, 28, of Abilene, Texas; Staff Sgt. Ryan D. Hammond, 26, of Moundsville, West Virginia; Senior Airman Quinn L. Johnson-Harris, 21, of Milwaukee; Senior Airman Nathan C. Sartain, 29, of Pensacola, Florida; and Airman 1st Class Kcey E. Ruiz, 21, of McDonough, Georgia.
Golden, Pierson, Hammond and Johnson-Harris were assigned to the 39th Airlift Squadron, Dyess Air Force Base, Texas. Sartain and Ruiz were assigned to the 66th Security Forces Squadron, Hanscom Air Force Base, Massachusetts.
It is not yet known what caused the crash at Jalalabad Airport near the Afghan-Pakistani border and whether hostile fire was involved, though the U.S. military in Afghanistan believes the latter to be unlikely.
"With high confidence, it does not appear at this time that enemy fire was involved in the aircraft crash. We have first responders on scene working at the crash site doing recovery operations," said Maj. Tony Wickman, a U.S. military spokesman, in an emailed statement to CNN.
However, the Taliban claimed that Islamist fighters downed the plane.
The plane "was shot down in an attack by Mujahedeen in Jalalabad city," Taliban spokesman Zabiullah Majahid said on Twitter.
Wickman said an investigation is underway to determine the cause of the crash.
The Jalalabad Airport, which has hosted the NATO-led International Security Assistance Force, has been subject to attacks by militants in the past.
The Lockheed C-130 Hercules, which has been in use since the 1950s, transports cargo.
President Barack Obama and Defense Secretary Ashton Carter put out statements on the crash Friday morning expressing sympathy for both the American and Afghan lives that were lost.
Carter said the Pentagon was "still trying to determine exactly what happened," but that in any case the incident was "a reminder of the risks that our men and women face serving their country in remote places all over the world."
Obama offered similar remarks.
"As we mark this terrible loss of life, we are reminded of the sacrifice brave Americans and our Afghan partners make each and every day in the name of freedom and security," he said. "Their willingness to serve so selflessly will not be forgotten."