Moscow said its aircraft had hit Islamic State (IS) command centers, arms depots and military vehicles, the report says.
Targets included the IS stronghold of Raqqa, but also Aleppo, Hama and Idlib - provinces with little IS presence.
Members of the U.S.-led coalition targeting IS have renewed their criticism of the Russian action.
In a statement, the U.S., UK, Turkey and other coalition members called on Russia to cease air strikes they said were hitting the Syrian opposition and civilians, adding that they would "only fuel more extremism."
The Syrian opposition and others have suggested non-IS rebel factions opposed to President Assad - the Kremlin's ally - are bearing the brunt of the Russian attacks.
Alexei Pushkov, the head of the foreign affairs committee in Russia's parliament, said the air strikes - which began on Wednesday - could last for three to four months.
He added that the U.S. had only "pretended" to bomb IS, and promised that Russia's campaign would be much more effective.
The British-based Syrian Observatory for Human Rights said Russian air strikes had hit a training camp and a camouflaged command post near the IS "capital" of Raqqa, and that 12 IS fighters were killed in the attack.
Activists and residents of the city said IS had cancelled Friday prayers and emptied mosques, amid fears of further Russian air strikes.
Elsewhere, a radio mast and communications tower belonging to the Free Syrian Army - forces opposed to President Assad which have received American training and supplies - were attacked by Russian aircraft in Aleppo. However, Syrian sources said neither had been destroyed, contrary to earlier reports.
Meanwhile, IS fighters have attacked a government airbase in eastern Syria.
Reports from the area, near the IS-controlled city of Deir al-Zour, speak of loud explosions, heavy clashes and government fighter jets circling in the sky.
The U.S.-led coalition said it had targeted IS in 28 air strikes in both Syria and Iraq on Thursday.