Among those who have confirmed their attendance in Moscow is Haneef Atmar, who is running against Ghani in the presidential elections, former warlord Atta Muhammad Noor and former Afghan president Hamid Karzai - both Ghani rivals - are also attending.
The Afghan foreign ministry, however, says the Russian government has been active behind the scenes to convince more Afghan politicians to take part in the meeting.
Still, Fawzia Koofi, a lawmaker and women's rights activist, said her participation in the talks was a good first step, even though she was one of only two women among the more than 20 Afghan figures who travelled from Kabul to Russian Federation.
A top USA general also said that Kabul must be involved in talks if a push for a peace deal is to be successful. The deal will ensure that terrorist groups are not allowed to use the country as a base of operations and that the USA and other foreign countries will withdraw their troops, Sputnik previously reported.
Mujahed added that at least 40 Afghan forces had been killed in Kunduz and Baghlan.
"A dynamic generation is working in Afghanistan and these are great achievements and we must defend them".
On the one hand, Moscow will burnish its credentials as a major player and mediator in the region; on the other hand, the United States withdrawal will increase risks of instability and violence in Central Asia, seen as Moscow's sphere of influence. He, however, added that the Afghan government does not consider the gathering to be in the interest of peace. He said on Twitter that Pompeo underscored "the centrality of the Afghan government in the peace process", and reiterated United States support for presidential elections set for July.
Sher Mohammad Abbas Stanikzai, head of the Taliban delegation, made a rare appearance in front of global media alongside Karzai after the talks.
Donald Trump will keep troops in Iraq to 'watch Iran'
Trump said the United States had spent " a fortune on the Al-Asad Air Base in western Iraq, and added: "We might as well keep it. Asked if that meant he wanted to be able to strike against Iran, Trump said , "No, because I want to be able to watch Iran ".
Trump said on Tuesday his administration had accelerated talks for a political settlement in Afghanistan and would be able to reduce USA troops there as negotiations advanced to end America's longest war.
Taliban is making "nice statements" in Moscow but back home schools for girls are closed in majority of Taliban-controlled areas Fawzia Koofi, a member of Afghan parliament and one of the two women participating in ongoing "inter-Afghan" talks in Moscow, told TRT World.
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.
"Today we had a very productive and good meeting, the Afghans who had differences with each other gathered here in order to reach a solution to end the problem in their common country Afghanistan and for lasting peace".
However, no Afghan government officials were present at the meeting, and Afghan President Ashraf Ghani strongly criticized the talks as undermining his government.
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".
He called for the release of Taliban detainees and claimed that USA and its protectorate regime have detained tens of thousands of Afghans and Taliban in their secret and open prisons.
While he said Moscow would not send troops to the country given the Soviet Union's painful experience in Afghanistan, Russia could provide other forms of assistance.
Such a meeting between the Taliban and Afghan politicians - including Karzai, who was appointed by the U.S. - is nearly unheard of.