The former Islamist leader al-Sharaa took over the rule of Syria in December last year, when the country's long-time dictator Bashar al-Assad was overthrown and fled to Russia.
The visit to Russia is al-Sharaa's first and on the agenda are meetings with several ministers, including President Putin, as well as talks about Russian investments and Russia's two military bases along Syria's Mediterranean coast, writes AFP.
The president will also formally request the extradition of the former dictator, according to a source for Reuters.
Since the change of power, Syria's new leadership has sought peaceful relations with Russia, which in 2015 intervened on Assad's side in the civil war.
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