"A wide number of questions regarding Saudi-Russia relations were discussed as well as the situation in North Africa and the Middle East," Kremlin spokesman Dmitry Peskov told Russian news agencies.
Peskov gave no further details about the talks in the Russian capital, which come amid strained relations between Moscow and Riyadh over the conflict in Syria.
Saudi Arabia has been strongly supportive of the rebels battling the regime of President Bashar al-Assad. But Russia, to the fury of Riyadh and its Western allies, has refused to cut its cooperation with the Damascus regime.
Widely regarded as among the most influential powerbrokers in the entire Middle East, Prince Bandar is the son of the late crown prince Sultan bin Abdul Aziz, who died in 2011.
Analysts believe that Saudi has regained the initiative from its much smaller neighbour Qatar in recent weeks to re-emerge as the diplomatic kingpin of the Gulf region.