BEIRUT, Lebanon — Israel has facilitated the evacuation of hundreds of rescue workers, known as the White Helmets, and their families from an embattled pocket of southern Syria, helping them to travel through Israeli-held territory to reach Jordan, Israeli and Jordanian officials said on Sunday.

The move in a part of Syria where pro-government forces are advancing followed a push by Western countries including the United States to protect members of the White Helmets, volunteer emergency workers who rush to the scene of airstrikes in civilian areas.

The Israeli Army said in a statement on Sunday that the United States and European countries had asked for help with the evacuation of the civilians “due to an immediate threat to their lives.”

A Foreign Ministry spokesman in Jordan, Mohammad al-Kayed, said that his country had authorized the United Nations to facilitate the entry of hundreds of Syrians to Jordan after Britain, Germany and Canada had made a “legally binding undertaking to resettle them within a specified period of time due to a risk to their lives.”