The rare public appearance that kicked off a day before saw Taliban officials spell out their vision for Afghanistan in front of rolling cameras and a host of political heavyweights, including former president Hamid Karzai.
Talks have mostly focused on a USA troop withdrawal and guarantees from the Taliban that Afghanistan would not again be used as a safe haven for terrorists to attack other countries, according to both Khalilzad and Taliban officials.
"At the first step, we want all the foreign forces to leave and end the military presence in our country", said Sohail Shahin, a spokesman for a Taliban office in Qatar.
"We do not know whether we will achieve an agreement - but we do know that after two decades of war, the hour has come to at least try for peace", Trump said.
"We agreed on many points and I am hopeful that in future, we can succeed more further, and finally we can reach a solution".
President Donald Trump told Americans on Tuesday his administration had accelerated talks for a political settlement in Afghanistan and would be able to reduce US troops there as negotiations advance to end America's longest war.
A US State Department spokeswoman said Washington had "not agreed to any timeline for a possible drawdown of troops".
The U.S. promised to withdraw half of its troops by April, the Russian state-run RIA Novosti news agency reported Wednesday, citing a Taliban representative in Moscow.
But the U.S. special envoy to Afghanistan, Zalmay Khalilzad, who led the United States side at the talks in Doha, Qatar, has repeatedly stressed that "nothing is agreed until everything is agreed".
"A more involved role for Moscow has surprised many, mostly due to Russia's bloody history in Afghanistan", said The Soufan Center, a nonprofit security analysis group.
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The Afghan Women's Network said their rights should not be used as a "political tool" in dealings with the Taliban, who barred women from schools and jobs and drastically curtailed their personal liberties when they ruled Afghanistan from 1996 to 2001. "If they (Taliban) return and impose restrictions on women, we will not accept that", Mashal Roshan, a coordinator from the Kabul-based women's network, told AFP.
"Ultimately, we need to get to a Taliban-Afghanistan discussion", General Joseph Votel, the head of US Central Command, told US lawmakers.
This comes as reports emerged earlier today that the deputy chief of the political office of Taliban in Qatar Mawlavi Abdul Salam Hanafi has said that the half of the US troops would withdraw from Afghanistan until the end of April.
However, the gathering has been criticized by Afghan President Ashraf Ghani.
Taliban and influential Afghan opposition leaders concluded a rare two-day "peace meeting" in Moscow on Wednesday, where they jointly declared that a complete withdrawal of US -led foreign forces was key to a lasting peace in Afghanistan.
Five policemen were also wounded and the Taliban seized all the weapons and ammunition from the security before reinforcements arrived, he said.
He added delegates agreed on "almost" everything - but a consensus was not reached over the Taliban's demand for an Islamic constitution, and the group's views on women.
It was also notorious for its treatment of women, banning majority from working or going to school.
But involvement of the Taliban in any government frightens many women, who recall the stifling restrictions under the Islamic insurgents.
Pentagon officials say they have no orders to withdraw troops.