A statement on the conference released by the Russian foreign ministry said that participants of the meeting agreed to continue consultations within the framework of this mechanism.
Taliban officials and Peace Council members have met at past forums elsewhere, and while no formal talks were ever held they have had some face-to face discussions.
Haji Din Mohammad Azizullah, head of the Kabul delegation, confirmed that he had "brief talks" with the Taliban members at a working lunch, characterising the talks as "friendly", according to Anadolu Agency. "But we didn't say that there will be any talks with the Taliban", he said.
USA officials have held two meetings with the Qatar-based Taliban negotiators since July. "But, of course, so far these negotiations are at a very early stage, we haven't reached an agreement yet", he said.
Afghan delegation member Hajji Din Mohammad told journalists that Russian Federation invited them to a new meeting but that "agreement was not reached on holding direct talks" with the Taliban, RIA Novosti news agency reported.
The conference was held at the level of deputy foreign ministers and related special representatives. "We took a considered decision to attend the meeting at a non-official level", he said.
Russian Federation has hosted talks with Taliban delegates and members of Afghanistan's high peace council, as the Kremlin seeks a role as peace broker between Islamist rebels and the US-backed government in Kabul.
A USA government watchdog last week said Kabul's control of Afghanistan had slipped in recent months as local security forces suffered record casualties while making minimal or no progress against the Taliban.
"We came here for a political solution".
In both cases, the U.S. has had an active military presence inside the countries.
The meeting drew considerable criticism from Kabul as it did not involve the Afghan government.
Calling New Delhi's claim that it's talking with Taliban along with other stakeholders in Masco to discuss Afghan issue as "laughable", MLA Langate Er Rasheed on Friday said that New Delhi stands exposed for its "hypocrisy, double standards and confusions".
"We asked them to define a date and place for the direct talks".
The meeting in Moscow helped move things in this direction, he added.
As well as the five-member Taliban delegation, Russian Federation brought to the meeting several senior Afghan political figures, including some who have clashed with Ghani in the past.
This time, the Afghan government hasn't sent its envoys, but members of the government-appointed Peace Council are attending the event.
Afghan Ambassador to Russia Qayum Kochai joined the group in Moscow. "It is clear that on the way to this goal it is necessary to overcome a lot of obstacles, including mutual grievances and mistrust accumulated by the parties", he said, adding that the objective of the talks was to create conditions favourable to "direct negotiations between the [Ghani] government, the Taliban Movement and representatives of the country's broad public and political circles".
According to the Russian Foreign Ministry, invitations to take part in the event had been sent to Afghanistan, India, Iran, China, Pakistan, the U.S. and some other countries.