Four of the British hostages are believed to be dead but a fifth, computer consultant Peter Moore, may be freed by his captives as a result of the U.S. move, The Times of London reported Wednesday.
The main demand of the group holding Moore was the release of 10 members held in U.S. detention.
Gen. Ray Odierno, the top U.S. commander in Iraq, says the release of between 300 and 400 members of Asaib al-Haq is part of a wider reconciliation process.
"We believe Asaib al-Haq has taken initial steps to reconcile with the government of Iraq," Odierno said.
He said active members of the group, whose name translates to League of the Righteous, are observing a cease-fire and have begun to turn in their heavy weapons.
Notable deaths of 2014 [PHOTOS]