Russia has hosted a landmark international meeting on Afghanistan in Moscow aimed at kick-starting peace talks after decades of war.
It is the first time Taliban militants have attended such an event.
Members of Afghanistan's High Peace Council, which oversees peace efforts but does not represent the Afghan government, were also present.
But the Taliban again stressed the group would only hold direct talks with the US - not the Kabul government.
Kabul did not send its delegation for the meeting, which was attended by about a dozen countries. The US had observer status.
"We discussed the subject of direct talks with the Taliban and asked them to choose the place and the starting time," said a High Peace Council spokesman, quoted by Russia's RIA news agency.
The Taliban have said the meeting is "not about negotiating with any side". Western officials and the Afghan government view the Moscow talks with some suspicion - some fear it could derail other efforts at negotiations.
So how big a deal is this meeting?
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 Afghan delegates, in Russia, with the US also in attendance is seen as significant.
Russia and the Taliban, for example, are historic foes, although they have begun talking in recent years.
US and Afghan forces have been fighting the Taliban in Afghanistan for more than a decade. And the US and Russia are former Cold War enemies who are still mistrustful of each other.
'It's a triumph for Russian diplomacy'
By Dawood Azami, BBC World Service
The Moscow meeting highlights Russia's return to the diplomatic forefront in Afghan affairs.
It's the first time that Moscow has invited the Afghan Taliban, who sent a high-level delegation. Neither the US nor the Afghan government wants Russia to lead such an initiative, known as the "Moscow Format".
But despite reservations by some, all 11 countries invited by Moscow are participating in different ways. Again, this is a first and unprecedented.
Although no significant breakthroughs were expected, bringing all the 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 on speaking terms with all players.
Who are the Taliban?
The Taliban emerged in the early 1990s following the withdrawal of Soviet troops from Afghanistan, shortly before the demise of the Soviet Union.
The militants went on to rule Afghanistan from 1996 to 2001, until they were driven from power by US-led troops following the 9/11 attacks, which the US blamed on al-Qaeda militants who were hosted by the Taliban.
The Taliban's power and reach have surged since foreign combat troops left Afghanistan in 2014.
They say their international status will be further strengthened by going to Moscow.
Research carried out by the BBC in January suggested that the Taliban were openly active in almost 70% of Afghanistan at the time, while being in control of 14 districts, or 4% of the country.
Are there other peace moves?
The US is engaged in its own direct talks with the Taliban and attending these meetings in Moscow is significant.
It turned down an invitation to the first meeting Russia hosted last year. But this time the US said a representative from its embassy in Moscow would attend to "observe the discussions".
The Taliban sent a five-member delegation 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 were held last month.
And there have been other signs of change. On Thursday, Pakistan confirmed it had freed a senior Taliban leader, Mullah Abdul Ghani Baradar, from jail last month at the request of the US.
"He was released to provide impetus to the peace and reconciliation efforts in Afghanistan," said a Pakistani foreign ministry spokesman.
In June the Afghan government and the Taliban agreed a three-day ceasefire to coincide with the end of the Ramadan fasting month, Eid.
How costly has the war been?
Given the high frequency and spread of Taliban violence, the Afghan security forces are overstretched and, in some cases, overwhelmed.
Afghan forces have been fighting hard to stop the Taliban's expansion. But their casualty rate remains alarmingly high and appears to be increasing.
Civilian deaths and injuries have also hit record highs. Casualty figures for the conflict, which began in 2001, are the highest since the UN started keeping records in 2009.