Ghani's allies in Washington insist Afghans should lead the peace process, and ostensibly the months-long push by the U.S. to engage the Taliban has been aimed at convincing them to negotiate with Kabul.
The Taliban has instead sat down at the table in Moscow with Ghani's main rivals, including Afghan politicians and warlords-turned-politicians who were once sworn enemies of the hardline Sunni Islamist group.
Karzai said the main issue under discussion in Moscow was that Afghanistan should be free of foreign forces, adding that there was a near consensus on this matter.
It was hard to find any influential critic of Afghan President Ashraf Ghani in Kabul on Tuesday - not because he has become popular among his opponents overnight, but because nearly all government critics are in Moscow to meet with Taliban representatives.
Fawzia Koofi, one of two women invited to Moscow, said the Islamist militants would "have to adapt to a modern Afghanistan".
If Pakistan plays a positive role in achieving a settlement to the conflict in Afghanistan, the USA will have opportunity and motive to help Islamabad fulfil that role, as peace in the region is the most important mutual priority for the United States and Pakistan, he said.
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). "But after ending their military presence, their non-military teams can come and we need them too, they can come and take part in the reconstruction and development process", he added.
Girls were banned from schools and colleges and women prohibited from the workplace save in a few areas such as medicine.
"The withdrawal will start from February 1 and continue until end of April", Hanafi told reporters in Moscow.
The gathering has been criticized by the office of current Afghan President Ashraf Ghani.
"They could hold a hundred such meetings, but until the Afghan government, the Afghan parliament and the legal institutions of Afghanistan approve it, it is just agreements on paper", Ghani said.
The Kremlin hosted another Taliban meeting in November past year which brought to the negotiating table representatives of the insurgent group as well as members of the Afghan peace council - a body created by the Afghan government to facilitate peace talks.
Mr Stanikzai said the Taliban had decided in Moscow to meet Afghan political figures who had "manpower" on the ground.
Their military partnership was "unwavering" and would remain until a lasting and inclusive peace was achieved, he said.
However, Mr Stanikzai said "women should not worry" about the prospect of increasing Taliban influence as they would seek to grant women all their "rights according to Islamic rule and Afghan culture".
A United States 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.
Efforts to find a negotiated end to Afghanistan's longest war have accelerated in recent months since the appointment last September of Zalmay Khalilzad as Washington's peace envoy. "But Afghans prefer a democracy which will be compatible to our values", said Qanooni.
"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 meeting was held at a Kremlin-owned hotel.