The Associated Press quotes two unnamed "high-ranking" Taliban leaders and Reuters quotes "sources" as confirming Omar's death as well as the selection of a successor — Mullah Akhtar Mansoor.
The Express Tribune of Pakistan also quoted the Afghan Taliban as acknowledging Omar's death, but in a statement quoted by the newspaper, the group appeared to dispute that he died in Pakistan.
"Mullah Omar never visited Pakistan or any other country except Afghanistan," the statement reportedly read. "Mullah Omar led his movement from Afghanistan."
The statement added: "Mullah Omar died owing to an illness some time ago and he died within two weeks of contracting the disease."
The selection of a successor for Omar was reportedly made at a Taliban shura, or official gathering.
Yehia Ghanem, a journalist who has long covered Afghanistan, tells Al-Jazeera. in an interview that Mansoor is a "key figure" in the Taliban organization who served as the governor of Kandahar before the U.S. invasion in 2001.
"He actually led many intelligence operations, very important and major ones," Ghanem is quoted by Al-Jazeera as saying.
Reuters says Siraj Haqqani, leader of the Haqqani militant network, will become Mansoor's deputy.
In 2010, The Wall Street Journal said Haqqani had "widened the use of suicide attacks, which became a Taliban mainstay only in the past few years."
It said Haqqani also "aided the Dec. 30  attack by an al-Qaeda operative that killed seven Central Intelligence Agency agents and contractors at a U.S. base in eastern Afghanistan, say militant commanders. And he orchestrated [the October 2009] assault on a United Nations guesthouse that killed five U.N. staffers, along with other attacks in the capital."