The comments from the Kremlin's envoy to Afghanistan came during talks in the Russian capital with the Taliban, with Moscow aiming to project influence over Central Asian and urge action against what it says is a growing threat of Daesh fighters in the region.
Taliban representatives ahead of Moscow met recently with European Union and US officials and travelled to Turkey to win official recognition and aid from the international community after their takeover of Afghanistan in mid-August.
The Kremlin's envoy to Afghanistan, Zamir Kabulov, said Wednesday that "of course" the question was raised, but that official acknowledgement of Taliban rule could only come when they "start fulfilling the expectations of the international community on human rights and inclusion".
The Taliban badly need allies as Afghanistan's economy is in a parlous state with international aid cut off, food prices rising and unemployment spiking.
Foreign Minister Sergei Lavrov, who addressed the gathering and criticised the absence of US officials, reiterated those concerns, saying "numerous terrorist groups" including Daesh and al-Qaeda have been seeking to exploit a security vacuum.
Lavrov noted the Taliban's "efforts to stabilise the military and political situation and set up work of the state apparatus."