“America especially should have undermined the notion that Mullah Omar was alive,” said Hajji Atta Mohammad Ahmadi, the head of Kandahar’s peace council. He said this would have helped uncover who actually led the Taliban, important information to “conduct peace talks from the standpoint of reliable knowledge.”

Yet for officials seeking peace negotiations, which are central to the long-term American hopes for Afghanistan, it was preferable that the insurgency possessed a clear hierarchy that could choose negotiators and decide terms. With Mullah Omar’s myth intact, the Taliban possessed that.

Moreover, any Taliban statements that sounded remotely like a peace overture were usually said to have Mullah Omar’s imprimatur. There was the time Mullah Omar was said to have sanctioned the opening of a political office in Qatar. And this year, Mullah Omar’s name was invoked during a nascent peace process, which stalled when his death was acknowledged last week.

“It doesn’t make sense to undermine a leader who sounds as though he is coming around to the idea of peace,” a senior analyst at the International Crisis Group in Kabul, Graeme Smith, said, offering an explanation for why diplomats might have gone along with treating Mullah Omar as alive and relevant.

Pakistani officials have also invoked Mullah Omar’s name. As Pakistani officials told Afghanistan in recent months that they would try to get a Taliban delegation to meet with the Afghan government, the Pakistanis, perhaps to lower expectations, added a caveat: It depended on Mullah Omar’s blessing, two Afghan officials familiar with the discussions said, speaking on the condition of anonymity to discuss diplomacy.

Pakistani officials deny that Mullah Omar ever lived in their country. But American and some, though not all, Afghan officials claim he had been living there for years. If it is true that Mullah Omar died in a Karachi-area hospital two years ago, it seems unlikely that Pakistani security officials would not have known he was dead even when they were evoking his name in the peace process.