The move comes during increased diplomatic efforts to revive stalled talks between the Taliban and the Afghan government, following the failure of a planned get-together in the Qatari capital Doha last month.
A Taliban delegation led by the movement's chief negotiator will visit Moscow this week to attend a ceremony expected to be followed by informal talks with senior Afghan politicians on the peace process, officials said on Monday.
The potential meeting comes during increased diplomatic efforts to revive stalled talks between the Taliban and the Afghan government, following the failure of a planned get-together in the Qatari capital Doha last month.
Taliban spokesman Zabiullah Mujahid said the 14-strong delegation, led by Mullah Baradar Akhund, will attend a ceremony on Tuesday marking the establishment of diplomatic relations between Russia and Afghanistan.
The delegation would also meet Afghan politicians and elders on the following day to discuss the future of the country, he said, without giving details.
It was unclear what Afghan officials will be present but former president Hamid Karzai is travelling to Moscow along with officials from his office, a spokesman said.
A spokesman for the Afghan foreign ministry said the Afghan ambassador in Moscow would attend the ceremony but it was unclear whether he would meet the Taliban delegation.
The Taliban have been talking with US diplomats for several months and have reached broad agreement on the withdrawal of international troops from Afghanistan.
But they have so far refused to talk to the Western-backed government in Kabul which they consider a foreign-imposed "puppet" regime.
To prepare the way for possible future peace negotiations, other countries have been trying to facilitate informal talks between the Taliban and representatives of civil society and state institutions.