The discussions concerned, according to a statement from the Syrian government, ensuring "accountability and achieving justice for the victims of the brutal war waged by the Assad regime".
The talks also dealt with how Russia "can rebuild trust" through concrete measures such as "compensation" and "reconstruction", according to the Syrian statement.
Russia, on its part, is trying to secure the fate of its naval base in Tartus and its airbase south of the coastal city of Latakia – both on the Syrian Mediterranean coast and Moscow's only military outposts outside the former Soviet Union.
Talks about the bases continue, according to Russian Vice Foreign Minister Mikhail Bogdanov, who led the delegation, according to the Russian state news agency Ria.
Syria's deposed president Bashar al-Assad fled to Russia in December when his regime was overthrown by rebel groups led by the Islamist movement Hayat Tahrir al-Sham, HTS, which now controls the country.
Russia, together with Iran, has been Assad's closest allies, and with military force helped him maintain power throughout the bloody civil war.