Thousands of people have fled rebel-held areas of southwestern Syria being targeted by government bombardment, a war monitor said on Thursday, as Damascus steps up attacks on an area near the border with Jordan and the Israeli-occupied Golan Heights.

The Syrian Observatory for Human Rights said some 12,500 people had fled opposition-held areas of northeastern Deraa province in the past 48 hours.

The war has pivoted towards the southwest since the Syrian government and its allies crushed the last remaining pockets of rebel-held territory near Damascus and the city of Homs.

Fighting in the southwest has been contained since last year by a "de-escalation" deal agreed by the United States and Russia, President Bashar al-Assad's most powerful ally.

A major government offensive in the area would risk an escalation of the seven-year-old war. The area is of strategic importance to Israel, which is deeply alarmed by Iranian influence in Syria.

Washington has warned it will take "firm and appropriate measures" in response to violations of the "de-escalation" deal.

Assad said earlier this month the government, at Russia’s suggestion, was seeking to strike a deal in the southwest similar to agreements that have restored its control of other areas through withdrawals of rebel forces.

But he also said there had been no results yet and blamed "Israeli and American interference". He said the territory would be recovered by force if necessary. Rebels have vowed not surrender "an inch" of the territory to Assad, one of their commanders said earlier this week.