The transfer of control of the prison has been a persistent source of tension between Afghanistan and the United States.
In a statement Wednesday, Karzai warned "any more delays could harm the bilateral relations."
However, a new statement from the presidential palace said Karzai has agreed with U.S. Secretary of Defense Chuck Hagel's request for an extra week to complete the handover of the prison, Khaama Press reported Sunday.
"In a telephone conversation with President Karzai, U.S. defense secretary asked for a week time for a complete transfer of the Bagram Prison to Afghanistan sovereignty," the statement said. "President Karzai agreed with the new time request and reminded Secretary Hagel that the transfer has been delayed several times in the past and that this time the handover should take place."
A previous planned transfer of the prison was delayed because the two sides couldn't agree on the terms of the handover.
Karzai has said he plans to release some of the prisoners after the transfer while United States officials said they wanted to make sure no dangerous prisoners were released.