Russia hosted an important international meeting on Afghanistan in Moscow, aimed at kicking off peace talks after decades of war.
It is the first time that Taliban militants have participated in such an event.
Also present were members of the Afghanistan Peace Council, which oversees peace efforts but does not represent the Afghan government.
But the Taliban again emphasized that the group would only have direct talks with the United States, not with the Kabul government.
Kabul did not send his delegation to the meeting, which was attended by about a dozen countries. The United States had observer status.
"We discussed the topic of direct talks with the Taliban and asked them to choose the place and time of departure," said a High Peace Council spokesman, quoted by the President. Russian RIA press agency.
The Taliban said the meeting "is not about negotiation anywhere". Western officials and the Afghan government look suspiciously at the Moscow talks – some fear it could derail other attempts at negotiation.
The countries also present in Moscow include China, Pakistan, Iran, India and Central Asia.
So, how big is this meeting?
The observers do not expect quick results from the Moscow talks – previous attempts at brokering a peace process have all failed.
But the fact that the Taliban are in the same room as the Afghan delegates, in Russia, with the United States present is considered significant.
Russia and the Taliban, for example, are historical enemies, although they have begun to speak in recent years.
The American and Afghan forces have fought the Taliban in Afghanistan for over a decade. And the United States and Russia are former Cold War enemies who are still wary of each other.
"It's a triumph for Russian diplomacy"
By Dawood Azami, BBC World Service
The Moscow meeting highlights the return of Russia to the diplomatic position in Afghan affairs.
It is the first time that Moscow has invited the Afghan Taliban, who have sent a high-level delegation. Neither the United States nor the Afghan government want Russia to lead such an initiative, known as the "Moscow format".
But despite the reservations of some, all 11 countries invited by Moscow participate in different ways. Again, this is a first and unprecedented.
Although no significant discovery was expected, bringing all relevant players under one roof is a huge success for Russian diplomacy.
Russia is in a unique position to host such a meeting as it is the only country where they talk to all the players.
Who are the Taliban?
The Taliban emerged at the beginning of the 1990s following the withdrawal of Soviet troops from Afghanistan shortly before the end of the Soviet Union.
The militants continued to govern Afghanistan from 1996 to 2001, until they were driven out of US-led troops after the September 11 attacks, which the US blamed on al-Qaeda militants who they were hosted by the Taliban.
The power and reach of the Taliban has increased since foreign combat troops left Afghanistan in 2014.
They say that their international status will be further strengthened by going to Moscow.
Research conducted by the BBC in January suggested that the Taliban were openly active in almost 70% of Afghanistan at the time, while they controlled 14 districts, or 4% of the country.
Are there any other peace moves?
The United States is engaged in its direct talks with the Taliban and participating in these meetings in Moscow is significant.
He refused the invitation to the first meeting with Russia hosted last year. But this time the United States said that a representative of his embassy in Moscow would "have witnessed the discussions".
The Taliban sent a delegation of five members from its political office based in Qatar.
It emerged in July that Taliban officials secretly met a senior US diplomat in Qatar. Another round of talks was held last month.
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And there were other signs of change. On Thursday, Pakistan confirmed that it had freed the head of the Taliban, mullah Abdul Ghani Baradar, from prison last month at the request of the United States.
"He was released to boost peace and reconciliation efforts in Afghanistan," a Pakistani foreign ministry spokesman said.
In June, the Afghan government and the Taliban agreed a three-day ceasefire coinciding with the end of the fasting month of Ramadan, Eid.
How much did the war cost?
Given the high frequency and spread of Taliban violence, Afghan security forces are overwhelmed and in some cases overwhelmed.
The Afghan forces have fought hard to stop the Taliban's expansion. But their rate of casualties remains alarming and appears to be on the rise.
Even deaths and civil accidents have reached record levels. The figures for the victims of the conflict, which began in 2001, are the highest since the United Nations began keeping records in 2009.
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