The White House on July 31 confirmed the death of Afghan Taliban leader Mullah Omar and said his demise "represents a chance for yet more progress on the path to a stable, secure Afghanistan."
The White House urged the Taliban "to heed [Afghan President Ashraf Ghani's] call for reconciliation and make genuine peace with the Afghan government."
The White House said it remains uncertain about the cause of the Taliban leader's death.
The Afghan president's office announced on July 29 that Mullah Omar died more than two years ago in a hospital in Karachi, Pakistan.
Afghanistan's National Security Directorate said that he died under "mysterious circumstances."
The Taliban said on July 30 that Mullah Omar died from an unspecified illness.
He had not been seen in public since the Taliban regime was ousted from power in late 2001.
The Taliban's main spokesman announced the selection of a successor, Mullah Akhtar Mansur, but the choice was reportedly rejected by Mullah Omar's son and powerful commanders in the militant group, suggesting there are significant divisions within the group.
On August 1, an audio message purportedly from Mansur, urged the Taliban to remain united and continue fighting.He did not endorse or reject peace talks with the Afghan government.
The authenticity of the message could not be independently verified.
A second round of talks, scheduled to begin July 31, has been postponed indefinitely.