“All around them in these graveyards are the regular Afghans — their graves are plenty,” Mr. Karzai said. “The dream of every mother, the hope of every father is buried there.”

Mr. Karzai was first installed as Afghanistan’s leader by the United States in late 2001, but the relationship soured. He has visited Russia often since leaving office in 2014, and in meetings with Mr. Putin and other officials he has aligned himself with Moscow’s view that the United States must leave Afghanistan, as the Soviet Union did.

Mr. Stanekzai, the Taliban’s chief negotiator, said in a speech lasting more than half an hour that the group did not seek to monopolize power inside Afghanistan. He said that they were pursuing an Islamist government, “in consultation with all Afghans,” and that the group did not recognize the country’s current Constitution, calling it copied from the West.

Perhaps the most revealing part of his speech came when he described the Taliban’s view of a future role for Afghan women. When in power, the group sent its religious police to patrol the streets, giving out lashes to women for, among other things, showing their ankles.

“We are committed to all rights given to women by Islam,” Mr. Stanekzai said. “Islam has given women all fundamental rights — such as trade, ownership, inheritance, education, work and the choice of partner, security and education, and a good life.”

Considering the group’s history, some Afghan women immediately questioned the statement’s sincerity.

But Fawzia Koofi, a female member of the Afghan Parliament and one of the two women in attendance, said she was happy to have heard the Taliban promise that women would not be stripped of their rights and would be allowed to serve as prime minister — though not as president.

However, she cautioned, “We have gained so much in the last 18 years, whatever the problems, that we do not want to go back the Taliban period.”