As many as 50,000 people have fled separate offensives against rebel forces in northern and southern Syria in recent days, activists say.
About 30,000 have left the northern town of Afrin as Turkish forces and their allies stepped up a siege.
In the Eastern Ghouta region outside Damascus, some 20,000 have left areas targeted by Syrian government forces.
The mass movements come seven years into a war which has driven nearly 12 million people from their homes.
At least 6.1 million are internally displaced while another 5.6 million have fled abroad.
More than 400,000 are believed to have been killed or are missing, presumed dead, since the uprising against President Bashar al-Assad began in March 2011.
Afrin, a city populated mainly by ethnic Kurds near the frontier, has been under bombardment from the air and the ground by Turkish forces and their local Syrian allies.
Some 30,000 people have fled the city and nearby villages, according to the Syrian Observatory for Human Rights, a UK-based monitoring group. They headed towards villages held by Syrian government forces.
Hundreds more families left overnight as shelling continued, the Observatory says.
Turkey is targeting the Kurdish People's Protection Units (YPG), a militia that it regards as an extension of the Kurdish rebels on its own territory.
Turkish President Recep Tayyip Erdogan told a gathering in Ankara that his country would not stop until its mission to capture Afrin had been completed.
According to the Observatory, nearly 20,000 civilians fled rebel-held areas in the Eastern Ghouta on Thursday as the government advance continued.
Pro-government forces are believed to have recaptured 70% of the region after three weeks of intense fighting against rebels there.
At the same time, 25 lorries carrying food aid entered the Ghouta town of Douma but the International Committee of the Red Cross (ICRC) said the aid was just a fraction of what was needed.
Turkey, Russia and Iran have sent their foreign ministers to the Kazakh capital Astana to prepare for a summit of leaders in Istanbul next month.
While Turkey is opposed to President Assad, Russia and Iran are the Syrian leader's closest allies..