State-run news agency SANA said the army entered Tabqa and its namesake military air base as well as the town of Ayn Issa, reports Xinhua news agency.
These areas are all under the control of the Kurdish-led Syrian Democratic Forces (SDF).
The development comes after a deal was reached on Sunday between the Syrian government and the Kurdish forces under the mediation of Russia to counter Turkey's military progress.
The Syrian army started to deploy troops toward Kurdish-controlled areas near the Turkish border after the deal.
On October 9, Turkey and its allied Syrian rebel groups launched a military operation to eliminate Kurdish forces in northern Syria, in order to end what Ankara perceives as the threat of "terrorists and separatists" on its southern border and to impose a safe zone for millions of Syrian refugees being hosted inside Turkey.
The offensive came after the US, the Kurds' main ally, pulled troops from the area, the BBC reported.
The US announced on Sunday it was evacuating all of its remaining soldiers from northern Syria.
The Turkish offensive and US withdrawal have drawn an international outcry, as the SDF were the main allies of the West in the battle against the Islamic State (IS) group in Syria.
There have been fears about a possible resurgence of the group amid the instability.
On Sunday Kurdish officials said nearly 800 relatives of foreign IS members had escaped from Ayn Issa, a camp in the north.
Turkey views elements of the Kurdish groups as terrorists and says it wants to drive them away from a "safe zone" reaching 32 km into Syria.
President Recep Tayyip Erdogan hopes to resettle up to two million Syrian refugees currently in Turkey within the zone. Many of them are not Kurds and critics have warned this could lead to ethnic cleansing of the local Kurdish population.
( With inputs from IANS )