Syrian authorities have not officially confirmed the theft.
AP writes that these are statues from the Roman era that stood in the museum's classical department, citing anonymous officials at the General Directorate of Antiquities and Museums.
AFP, for its part, reports that the thieves came across ancient gold objects, according to information from security sources.
Sources seem to agree that the theft involved six items and that it took place during the night of Monday. In the morning, the door to the department was found broken open.
The museum is temporarily closed to investigate the incident.
The National Museum in Damascus houses the country's largest collection of ancient artifacts. After the chaotic years of war, security has recently been tightened, including the installation of metal detectors and surveillance cameras.
