Taliban militants who are in control of parts of Baghlan province have not commented on the attack.
Abdullah Abdullah, the country's chief executive, said Monday that the Afghan government should be at the centre of any peace talks, adding that Kabul "would prefer the Moscow meeting had a different shape".
The two-day talks is the first time a Taliban delegation has officially met with senior Afghan politicians, although the participants were not representing the government.
It was the second time President Ashraf Ghani was frozen out of such talks in recent weeks after the U.S. held entirely separate discussions with the insurgents in Doha without Kabul.
He said a formal Taliban office in Afghanistan and a credible guarantee for peace was vital.
Khalilzad, who also did not attend the Moscow meetings, is due to speak in Washington on February 8 about the status of the Afghan peace process.
Lead Taliban negotiator Sher Mohammad Abbas Stanikzai told reporters that the movement did not want to rule alone but as part of "an intra Afghan Islamic system of governance ... in consultation with all Afghans".
He should, because right now, the situation is this - the opposition, which in theory holds no authority to govern, is holding "peace talks" with declared enemies of the state, and will likely skate through without any possible punishment. "We can find complete peace in Afghanistan".
U.S. President Donald Trump said on Tuesday that he'll reduce the American military presence in Afghanistan.
Ghani also questioned the mechanism of the Moscow Talks and said: "With whom, what will they agree upon there?"
U.S. and Taliban delegations met in Qatar in January and are due to meet again this month.
One effect of reduced USA leverage is a greater role for Moscow, which has worked behind the scenes to solidify influence in Afghanistan.
The meeting has sidelined Afghan President Ashraf Ghani's government, which has criticized the gathering. USA forces in 2001 toppled the country's hardline Taliban leaders for harboring the al Qaeda militants responsible for the September 11 attacks. "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.
"I would characterize where we are in the process as very, very early in the process", U.S. General Joseph Votel, head of the U.S. military's Central Command, told a Senate hearing. "And we will indeed focus on counter-terrorism", Trump said.
The Moscow Talks has drawn a mixed response from members of the public with some saying the two-day meeting between influential Afghan politicians and members of the Taliban could help the peace process, while others say the talks could have a negative impact on the process. The quid pro quo for the Taliban to officially and finally break ties with al-Qaeda and its affiliates could be the withdrawal of American soldiers.
Under their brutal interpretation of Sharia law, the Taliban confined women to their homes, only allowing them outside with a male escort and hidden beneath a burqa.
The group was notorious for its treatment of women, banning majority to work or go to school.
In the Russian capital, in scenes unthinkable under their regime, the Taliban sat and listened as women defended their hard-earned freedoms in a modern Afghanistan.
While Moscow has sought to distance itself from the conference, calling it an initiative of the Afghan diasporas, few doubt the Kremlin's deep involvement.
According to reports, the Taliban indicated that they want to amend the current Afghan constitution which they see as invalid and import of the West.
"We need to make sure everything they say here, they mean it", Ms Koofi added.