The Taliban has killed at least 47 people in separate attacks in Afghanistan, as they demanded a new constitution and promised an "inclusive Islamic system" to govern the war-torn country at a rare gathering with senior Afghan politicians in Russian Federation on Tuesday that excluded the Kabul government.
Mr Stanikzai said the Taliban had decided in Moscow to meet Afghan political figures who had "manpower" on the ground.
He also stated that the two sides hope to achieve a durable peace in the war-ravaged country.
A Taliban official said on Wednesday the United States had promised to withdraw half of its troops from Afghanistan by the end of April, but the USA military said no timeframe had been set.
USA negotiators have tried to persuade the Taliban to meet Afghan officials, but Mr Stanikzai remained vague when questioned about the circumstances under which they would ever agree to do so.
Along with Karzai, the former president, numerous 38 delegates from Kabul have held prominent government positions. Votel also said the United States would need to continue to support Afghan security forces financially even if USA troops withdrew.
In addition to a Taliban delegation, it was also attended by former Afghan President Hamid Karzai, as well as other high-profile opposition figures.
In a lengthy interview with the privately owned ToloNews TV, Ghani denounced the ongoing Moscow meeting, arguing the attendees did not have the executive power to translate decisions into action. After years of being on the fringes since the invasion of the Americans and their allies ousted them from power, the Taliban are now gaining acceptance as legitimate stakeholders in the Afghan political process.
The Taliban have claimed both attacks.
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A USA general told a Senate hearing shortly before Ghani's interview was broadcast that the talks were in their early stages and the Afghan government would have to be part of any negotiated solution. "We can find complete peace in Afghanistan".
Ghani meanwhile gave his assurance that presidential elections will be held on time. "They can say what they want", the Afghan president added.
The absence of Afghan government representatives at the talks have underscored the Taliban's hostility toward Afghan President Ashraf Ghani's increasingly marginalised administration in Kabul.
Earlier on Monday, the Taliban targeted a local pro-government militia in a village in northern Samangan province, killing 10 people, including a woman, said Sediq Azizi, spokesman for the provincial governor.
After 17 years of war in Afghanistan, Trump praised "the unmatched valor" of US forces.
Uzbekistan has once again expressed its readiness to host any direct talks between the government of Afghanistan and the Taliban movement, the Uzbek Foreign Ministry said on Tuesday.
The US-Taliban talks have revolved around a pullout of foreign troops in return for a guarantee from the insurgents that Afghan soil will not be used against US interests by militant groups such as al-Qaeda and affiliates of Isis (Islamic State).
Karzai and other Afghan leaders were confident that the Moscow siting will pave the way for start of an intra-Afghan dialogue. The insurgents recognize that while they may never be able to defeat the United States militarily, neither can the USA completely pacify the insurgency.
United States 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.