The escalation comes a day after the US shot down a Syrian air force jet.
In a statement, the Russian defence ministry said that starting on Monday it will track all jets and drones from the coalition in the area.
And it has demanded a full account of why the US military shot down the Syrian SU-22.
Areas of northern Syria west of the Euphrates were controlled by Islamic State until recent months when Syrian government forces captured most of the region back.
US Central Command confirmed that one of its F-18 Super Hornets downed the Syrian aircraft, which it said had dropped bombs near the American-backed Syrian Democratic Forces (SDF).
The Kurdish-led SDF – which is aligned with the US in the campaign against IS – had warned Syrian government forces to stop their attacks or face retaliation.
The downing of the warplane is the first time in the conflict that the US has shot down a Syrian jet.
Syria said that the fighter jet that was downed was on a combat mission against Islamic State.
Russia, a key ally of Syrian President Bashar al Assad, has been providing air cover to the government’s offensive since 2015.
Clashes between the SDF and Syrian government forces have been rare, with some rebel groups even accusing them of coordinating on the battlefield.
Both sides are battling IS – with SDF fighters focusing on the northern city of Raqqa and government forces attacking IS in northern, central and southern Syria.