'Its clear all sides want to end the war,' said US Special Representative for Afghanistan Reconciliation Zalmay Khalilzad.
Talks are expected to resume March 2 after a short pause for 'internal deliberations'.
US envoy Zalmay Khalilzad and Mullah Abdul Ghani Baradar, a Taliban deputy leader and a co-founder of the group, have conferred for the first time.
Russia should pay restitution to the Afghan people, rather than meddling in Afghanistan's internal affairs and supporting the Taliban, local officials and analysts say.
The recent 'peace talks' were set up by Russia's intelligence service, not Afghans living in Russia, as the Kremlin tried to spin.
The goal of the delegation to bring 'all Afghan parties together in an intra-Afghan dialogue', the US State Department said.
'Looking for peace in an enemy's home is not the right thing to do,' a religious scholar in Herat said.
The meeting between Afghan opposition politicians and the Taliban in Russia 'is nothing more than a fantasy', President Ashraf Ghani said.
Head of US Central Command Gen. Joseph Votel and US Secretary of State Mike Pompeo underscored the importance of reaching a Taliban-Afghanistan discussion.
A second meeting in Moscow -- this time between Taliban representatives and Afghan opposition politicians -- is yet another attempt by Russia to sabotage the peace process.