The clash between the rebels and the security forces lasted two hours.
The Taliban's statement in Moscow is clearly meant to dispel the memories of women being beaten and murdered under its brutal theocratic rule, as well as forced into burqas and barred from leaving their homes without a male relative as escort.
The leader of the Taliban's peace negotiations with the U.S. says the insurgents do not want to seize "the whole country by [military] power".
Up to 10 local police personnel were killed as anti-government militants stormed security checkpoints in northern Baghlan province on Tuesday, a local official said on the condition of anonymity.
Afghan authorities rarely make public their battlefield casualties.
They argue that Ghani seeks to spoil this rare opening for peace and that his resistance derives from a fear that if talks progress, he could lose his chance for five more years in power.
Karzai, who was the first president of Afghanistan under United States and served till 2014, admitted the absence of Kabul officials from the Moscow talks was not helping the peace process, but remained hopeful.
Ghani's administration shunned the February 5-6 Russian-hosted initiative, which came after the US announced it was close to reaching a framework agreement with the Taliban on ending the 18-year Afghan war, including on the withdrawal of foreign troops.
Head of the Taliban delegation, Sher Mohammad Abbas Stanikzai said the two sides agreed on many points, and chose to continue talks in the future.
"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 interim government should also pave the way for a transparent election", Atta Muhammad Noor, an influential former warlord, said on Twitter.
But the meeting has sidelined Afghan President Ashraf Ghani's government, which has criticized the gathering. The insurgents recognize that while they may never be able to defeat the United States militarily, neither can the USA completely pacify the insurgency.
The meeting, ostensibly organized by members of the Afghan diaspora in Russian Federation, also carried a quasi-official imprimatur.
One effect of reduced USA leverage is a greater role for the Kremlin, which has worked behind the scenes to solidify influence in Afghanistan. The organizers say in case of success further meetings could be held.
Underscoring the longtime conflict, the Taliban attacked an army base in the northern city of Kunduz as the Moscow talks were underway, killing 26, mostly soldiers and policemen. Domestic television coverage of the event was virtually non-existent. "Venue for negotiations and a communication site in the shape of an office is necessary for peace", he said, adding at present the Taliban have no open and formal address as a venue for negotiations which is a preliminary requirement.
The Taliban have always refused to break bread with Ghani and Kabul, who they view as United States stooges.
The Taliban consider Ghani and his administration to be U.S. puppets, and have refused offers to talk a truce.
Russian Foreign Minister Sergey Lavrov, apparently responding to the criticism, has reiterated his government's committed to help in a political settlement to the Afghan conflict.
Karzai and other Afghan leaders were confident that the Moscow siting will pave the way for start of an intra-Afghan dialogue. It is in the interests of the Afghan people as a whole that they should be included and heard, and their fundamental rights recognised.