The Embassy which has handled US interests in Syria since 2012 has also warned the 71-year-old to be careful due to anti-American sentiment and the risk of car bombings and other attacks.
Although Webber said there is no way he is leaving.
Webber teaches English in a high school in Damascus and several times a week shares his love of Charles Dickens with teenagers from the French-speaking Lycee Charles-de-Gaulle.
He was born and raised in Orchard Park, New York, a suburb of Buffalo. His father was a German railyard master and his mother was a Polish nurse.
He was living in California when he was offered a job teaching science at Damascus Community School, a private American academy.
Webber arrived in Damascus in 1975, and went on to convert to Islam and marry a Syrian woman. Except for a brief stint teaching in Iran, he has lived in Syria ever since.
In the chaotic early months of the conflict when foreigners fled, fearing kidnappings and bombings, Webber and his wife began taking strong precautionary measures which included doing a lot more together so they weren't alone and checking the car for bombs.
The security situation in the capital has improved since then, and over the past week a US and Russian-brokered cease-fire has brought about the first major lull in the fighting.
Although Webber has no plans to leave the place he has called home for more than four decades.
