A Taliban official said on Wednesday that no timetable had been agreed with the US government for the partial withdrawal of USA forces from Afghanistan, and that negotiations were still underway.
Still, Fawzia Koofi, a lawmaker and women's rights activist, said her participation in the talks was a good first step, even though she was one of only two women among the more than 20 Afghan figures who travelled from Kabul to Russian Federation.
The Taliban control almost half of Afghanistan, and are more powerful than at any time since the 2001 US-led invasion after the 9/11 terror attacks.
Debate: What future for Afghanistan without U.S. troops?
If the Taliban have any complaints, however, it is President Trump's talk during the State of the Union address of leaving behind forces for "counter-terrorism" operations.
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In a joint statement issued after the negotiations, they also agreed to support peace talks in Doha with American negotiators.
"This meeting here in Moscow, it was very successful, and we agreed on many points", Stanikzai told reporters at the end of the two-day deliberations.
Earlier Wednesday, a senior Taliban official told reporters the US had agreed to withdraw half its ground troops by the end of April - a claim refuted by North Atlantic Treaty Organisation and the US State Department.
He said there was no detailed agreement with the US chief negotiator Zalmay Khalilzad who has been meeting separately with Taliban negotiators.
Meanwhile, as the talks were underway in Moscow, violence continued in Afghanistan.
In an interview to Tolo News before the Moscow talks, President Ghani said the Afghan politicians participating in Moscow talks lack "negotiating authority". If the United States continues to show that it is in a hurry to leave Afghanistan, then the Taliban would be more than happy to wait them out.
Both sides have indicated that a number of issues still need to be resolved.
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The US held peace talks with the Taliban in Qatar last month that ended with signs of progress towards the withdrawal of thousands of foreign troops from Afghanistan and an end to more than 17 years of war.
"The people who are in Moscow, including the Taliban and Afghan politicians, have one thing in common: they are all against Ghani", Yunus Fakur, a Kabul-based Afghan analyst, told DW. Today, we have a meeting in Moscow which ostensibly undermines the US-backed regime in Kabul.
The meeting brings together Taliban representatives and Afghan figures including former President Hamid Karzai, opposition leaders and tribal elders - but not Kabul government officials. India had sent retired officials to the Russia-led peace talks in November 2018 where the Taliban representatives were also present.
The Taliban governed Afghanistan in 1996-2001 with an ultra-conservative and often brutal interpretation of Islamic law.
It was also notorious for its treatment of women, banning a lot of them from working or going to school. While the Taliban's return to power is not a given, chaos is the most likely outcome.
The Taliban, responding to Trump's speech, rejected any suggestion of a lingering USA focus on counter-terrorism after troops are drawn down, reiterating their long-held demand that all foreign troops get out.
Taliban leadership is rarely seen in public and scenes of Taliban officials clad in black turbans outlining their manifesto for live television is virtually unheard of.
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