MOSCOW—Russia has sent a few dozen special-operations troops to Syria in recent weeks, Russian and Western officials say, redeploying the elite units from Ukraine as the Kremlin shifts its focus to supporting Syrian President Bashar al-Assad.

Russia in late September launched a campaign of airstrikes in support of Mr. Assad’s government, and President Vladimir Putin has said Russian troops won't play a role in ground combat. But Russian military experts and officials say small numbers of special-forces units—whose missions...