The meeting comes days after Russia vetoed a draft UN resolution that would have referred crimes committed in Syria to the International Criminal Court (ICC).
Assad expressed "his appreciation for the Russian position of support for the Syrian people in their war against terrorism," state news agency SANA said, using the government's term for its opponents.
Two weeks away from a controversial vote that is expected to return him to power, Assad stressed "the significance of Russia defending global stability in the face of the West, which is trying to impose its hegemony in the region", SANA added.
Moscow has backed Damascus financially, politically and militarily ever since the outbreak of a revolt demanding political change in Syria in March 2011.
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The uprising morphed into an insurgency after Assad's regime unleashed a massive crackdown on Arab Spring-inspired protests.
More than 160,000 people have been killed in the conflict and nearly half the population has been forced to flee their homes.
On Thursday, Russia and China vetoed a draft UN Security Council resolution that would have referred the situation in Syria to the ICC, and that could have seen war crimes committed by all sides in the conflict investigated.