The clashes came as Taliban and Afghan opposition leaders gathered in Moscow for what organizers said would be a two-day "intra-Afghan peace meeting" to discuss recent peace building efforts in Afghanistan.
A Taliban official said on Wednesday the United States had promised to withdraw half of its troops from Afghanistan by the end of April, but the U.S. military said no timeframe had been set.
The push for peace comes as the Taliban, ousted by USA -led forces in 2001, have staged near daily attacks and are in control of or contesting districts across almost half the country.
But perhaps adhering to the maxim that in global relations and statecraft there are no permanent friends or enemies, all parties that attended the Moscow conclave are working to protect their permanent interests in Afghanistan.
The Afghan government was not represented at both the talks in Doha and Moscow, sparking fears among many Afghans that a hasty pullout of USA troops would once again plunge the war-ravaged country into a brutal civil war.
The Taliban killed at least 21 people in their latest attacks in Afghanistan, including 11 policemen who were slain when the insurgents stormed a checkpoint in northern Baghlan province, provincial officials said Tuesday.
Afghan Foreign Ministry Spokesman Sebghatullah Ahmadi told VOA the Moscow meeting has no legitimacy and the government will not accept any possible outcome of the discussions.
According to two Afghan dailies, Kabul's absence from the Moscow gathering further "isolates Ghani" and "sabotages the authority of the Government".
Lead Taliban negotiator Mohammad Abbas Stanekzai speaks at a conference arranged by the Afghan diaspora in Moscow on Tuesday.More news: Feuding UK politicians seek elusive unity as Brexit looms
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Taliban spokesperson Mohammad Abbas Stanikzai made a rare appearance in front of global media.
It was the second time President Ashraf Ghani was frozen out of such talks in recent weeks after the USA held entirely separate discussions with the insurgents in Doha without Kabul. "We can find complete peace in Afghanistan". THey were armed with modern weapons to launch quick attacks, he added.
USA and Taliban delegations met in Qatar in January and are due to meet again in February.
However, no Afghan government officials were present at the meeting, and Afghan President Ashraf Ghani strongly criticized the talks as undermining his government.
He said that "when the American forces announce the withdrawal of their troops" there could be further "intra-Afghan dialogue".
The Russian foreign minister was directly referring to last months' six-day negotiations USA reconciliation envoy Zalmay Khalilzad held with Taliban officials in Qatar.
A ceasefire 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-Qaida and Islamic State to attack the United States and its allies.
As part of any negotiated settlement, the United States will push the Taliban to distance itself from al-Qaeda and other terrorist groups.
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.
America's longest-running war is edging closer toward a conceivable end.