The talks, which draw officials from 10 countries including China and Pakistan, are one of the Taliban's most significant international meetings since seizing power in mid-August.
They come after Russian President Vladimir Putin warned last week that Daesh fighters were gathering in Afghanistan to spread discord in former Soviet republics flanking Russia.
Russia's veteran foreign minister, Sergei Lavrov, is set to address the gathering.
The Taliban delegation is headed by Deputy Prime Minister Abdul Salam Hanafi, a senior figure in the new Afghan leadership who led talks with the European Union and the United States last week.
Those followed talks in Ankara between the Taliban and Turkish officials.
Brussels has pledged one billion euros ($1.2 billion) to avert a humanitarian crisis after the hardline group's takeover.
Russia's foreign ministry said on Tuesday that one of the aims of the Moscow meeting was to consolidate the "efforts of the international community to prevent a humanitarian crisis".
Moscow also said the formation of an "inclusive government" would be on the agenda, and that parties to the talks were expected to release a joint statement afterwards.
Moscow has reached out to the Taliban and hosted its representatives in Moscow several times in recent years, even though the Taliban is a designated terrorist organisation in Russia.