A Taliban official said on Wednesday the United States had promised to withdraw half of its troops from Afghanistan by the end of April, the RIA news agency reported, but Washington said no time-frame had been set.
But the US -backed government in Kabul was not invited to the conference because the Taliban have persistently refused to engage in any talks with Kabul until all foreign forces leave Afghanistan.
Despite the absence of any Afghan government representatives, the Moscow meeting has been described as part of an "intra-Afghan" peace process.
However US President Donald Trump has made clear his desire to bring an end to the 17-year conflict and withdraw at least the vast bulk of American forces.
However, Stanikzai said "women should not worry" about the prospect of increasing Taliban influence in the country as they would seek to grant women all their "rights according to Islamic rule and Afghan culture". But the Afghan leader has lost that luxury in recent months as he has openly opposed the outcome of US-Taliban talks, led by US special envoy Zalmai Khalilzad.
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A ceasefire and the withdrawal of thousands of US -led North Atlantic Treaty Organisation troops is on the table after Washington secured earlier assurances from the Taliban that they would not allow groups such as al Qaeda and Islamic State to attack the United States and its allies. But if the assessment was that Afghanistan is going to be critical for Indian interests in the region and beyond, then New Delhi should have been better prepared by now to protect its significant investments there.
"Thanks to their bravery, we are now able to pursue a possible political solution to this long and bloody conflict", Trump said.
"We look to regional actors such as Pakistan to cease behaviour undermining regional stability and play constructive role in achieving peace in Afghanistan as well as the whole of South Asia", General Votel told members of the Senate Armed Services Committee.
US-led forces in 2001 toppled the hardline Taliban for harboring the al Qaeda militants responsible for the September 11 attacks.
The gathering has been criticized by Afghan President Ashraf Ghani.
The rigid insurgent stance also forced Washington to exclude Ghani's government from talks between USA and Taliban officials seeking a political resolution to the conflict.
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This comes after a senior Taliban member and deputy head of their Qatar office said on Monday, after the first day's session, that the group would talk to the Afghan government once a timeline was set for the complete withdrawal of United States forces from Afghanistan.
"They arrived there late, fought back and managed to get the checkpoint under control of the check point, " he added.
But involvement of the Taliban in any government frightens many women, who recall the stifling restrictions under the Islamic insurgents. "We can find complete peace in Afghanistan".
"Peace talks with the Taliban continue, but (the Defense Department) has not received a directive to change the force structure in Afghanistan", Manning said.
US officials say any withdrawal is contingent on a ceasefire - something the Taliban insists on happening first - and that the movement must be prepared to enter talks with the Afghan government to help create a durable peace.
"When Mr. Karzai returns from Moscow we will see what he has brought".
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The Taliban has been carrying out bloody attacks against civilians and security forces with hundreds killed since the beginning of the year alone.