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.
The Taliban entered the second day of unprecedented talks with powerful Afghan politicians in Moscow on Wednesday, sidestepping the Kabul government.
Former Vice President Mohammad Yunus Qanuni and former Balkh Governor Atta Mohammad Noor are also on the list of participants, along with former Taliban insurgents who reconciled with the Afghan government.
Pompeo emphasised on the important gains made by the Afghan people since 2001 and U.S. desire for a long-term partnership with Afghanistan, the State department Deputy Spokesperson said.
The Taliban demanded a new constitution for Afghanistan 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.
Fawzia Koofi, one of two women invited to Moscow, said the Islamist militants would "have to adapt to a modern Afghanistan".
Karzai, who was the first president of Afghanistan under U.S. and served till 2014, admitted the absence of Kabul officials from the Moscow talks was not helping the peace process, but remained hopeful.
A cease-fire 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. "We wish that they would have been here today". The Taliban closed girls' schools and banned women from working under their regime, but have indicated they could loosen some guidelines in line with Sharia law.
On an April withdrawal, he said: "It's our desire". President Ashraf Ghani insists that a final agreement must protect the inalienable rights and values of Afghans.
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He said guarantees had been given that future production of the Juke and Qashqai models were not affected. The letter said United Kingdom support was contingent on Nissan building two models in England.
"We clearly recognize that they (Afghan government) have to be a part of this solution and must be in the negotiation aspects of this, we can't do that on their behalf". The delegation will be led by Mohammad Abbas Stanikzai, former head of Taliban's Qatar office.
Representatives of the Taliban met with other Afghan delegates in Moscow to discuss the prospects of peace and the removal of all foreign troops from Afghanistan.
Going into the negotiating room in Moscow on February 5, Stanikzai did not respond to questions from journalists about the Taliban's position on direct talks with an intra-Afghan delegation - saying that "comments will come later".
The militants have indicated they would provide a safe environment for women's work and education under an "Islamic system" they have proposed for Afghanistan's future.
Their current chief negotiator, Sher Mohammad Abbas Stanekzai, painted a picture of the group's current view of the role of women in society, rejected the current Afghan constitution and called for the end of USA presence in Afghanistan.
"If you guys can eat together, laugh and pray together, hug each other why you are still killing innocent Afghans?" one Facebook user posted.
The Afghan government fears that after the possible departure of the foreign military the Taliban won't have reasons to take part in the peace talks.
The conference, hosted by an Afghan diaspora group, was welcomed as "useful" by Russian Foreign Minister Sergei Lavrov in a statement. "Let hundreds of such meetings be held". Pompeo also emphasised the importance of an intra-Afghan dialogue and the inclusion of the Afghan government in peace talks with the Taliban, according to Palladino.