The approval came at a National Security Council meeting on Thursday.
CNN reported over the weekend that the President also emphasized to his team that the U.S. would continue to support the Syrian opposition as Russia enters the war-torn country.
"President Obama was clear that we intend to continue our efforts to degrade and ultimately destroy ISIL in Syria and to keep supporting the moderate Syrian opposition," the official said, using another name for ISIS.
While Russia has said that it is conducting military operations to wipe out ISIS, U.S. officials have questioned that aim given that many of its airstrikes have not targeted places ISIS is active. Instead, they have seen the effort mostly as a move to bolster close Moscow ally President Bashar al-Assad.
The latest U.S. assessment of Moscow's activity in western Syria indicates Russia has moved several ground combat weapons and troops into the area to potentially back up Syrian forces in the field planning to attack anti-regime forces, according to two U.S. defense officials.
The U.S. views the move as Russia "stepping up its ground activity" in Syria to attack those forces, rather than ISIS elements, according to one of the officials.
It's believed the Russians are positioning the weapons to be able to support a Syrian ground offensive, the officials said.
The equipment includes several piece of artillery, as well as four BM-30 multiple-launch rocket systems -- all considered to be highly accurate weapons. The latter is capable of rapid-fire rocket launches.
Several weeks ago, Russia moved about half a dozen artillery pieces into Latakia port.
The U.S. originally had thought that might be for defense of the port, but the latest move is an indication of potential ground attacks in the coming days, the official said.
The weapons have been spotted between Homs and Idlib and west of Idlib.
It is not clear if they're now in final position for possible artillery strikes.
The officials also said that Russia has moved electronic jamming equipment into Syria. Both a truck-mounted system and a number of pods that can go on aircraft have been observed. This could potentially give the Russians the ability to jam electronics of coalition aircraft.