"The security situation continues to be unstable and unpredictable with active clashes between armed groups throughout the country", warns the US State Department in a security message published on social media.
"Leave Syria now while commercial alternatives are still available in Damascus", writes the department.
Fighting jihadists are advancing in Syria. The offensive, led by the Islamist group Hayat Tahrir al-Sham (HTS), has rapidly advanced south towards Syria's third largest city Homs.
The Foreign Ministry in neighboring Jordan urged its citizens to leave Syria "as soon as possible" on Friday. The same day, Jordan closed its border crossings to and from Syria.
The Islamist rebels had previously taken control of Syria's fourth largest city Hama, just north of Homs, as well as Aleppo in the initial offensive.
The city of Daraa in the south is also reported to have been taken over by local factions, which according to SOHR now control large parts of the province with the same name.
Fighting is also reported from the border with Jordan.
On Friday, reports also emerged that Kurdish-led forces, which had received support from the US in the fight against the terrorist sect IS, had crossed the Euphrates River in Deir al-Zor province in the east. This after regime forces had left the area to head west towards Homs.
US Secretary of State Antony Blinken is seeking a "political solution to the conflict" in a conversation with Turkish Foreign Minister Hakan Fidan. Blinken also emphasized, according to his spokesperson, that civilians and minority groups in the war-torn country must be protected.