Mr. Baradar was a moderate on social issues and argued for maintaining relationships with the West and Afghanistan’s neighbors. The hard-liners among the Taliban under the influence of Osama bin Laden had forced Western aid agencies to leave Afghanistan, and the country faced a severe famine and economic crisis. Mr. Baradar argued against isolating Afghanistan and cutting off all aid. He was aware of his country’s dependence on financial aid from the West.

Although he had opposed the presence of bin Laden in Afghanistan after Mullah Omar gave him sanctuary in 1996, Mr. Baradar stayed close to Mullah Omar in Kandahar after their regime fell.

Owing to his impeccable record of service to the Taliban cause, no other Taliban leader will be able to contradict Mr. Baradar if and when he takes steps toward peace. He is also the most likely figure to sell peace to the more militant Taliban commanders, who are inclined to continue fighting and want to claim total victory and impose a Shariah system on the country as they did in the 1990s.

The United States will benefit from his presence in the Qatar talks, as Mr. Khalilzad and his colleagues will be speaking to a prominent and decisive Taliban leader who can make decisions.

Mr. Khalilzad’s team has made significant headway, and American and Taliban officials have “agreed in principle to the framework” of a peace deal in which the Taliban promise not to host terrorist groups in the future and to help the United States rid Afghanistan of the remnants of Al Qaeda and the Islamic State. The deal could lead to a full pullout of American troops in return for a cease-fire and Taliban talks with the Afghan government.

Major questions remain to be resolved. The Taliban want an American troop withdrawal announced and their prisoners freed from Afghan jails as an immediate first step. The Americans have won a pledge from the Taliban that Afghan soil will never be used again by terrorist groups. The United States is also insisting on a Taliban cease-fire with both American and Afghan forces and an agreement to start talks on the future political setup with President Ashraf Ghani and the Kabul government.