Around 1,200 Hezbollah fighters are estimated to have been killed in the Syrian conflict.
Hundreds of families were fleeing the area because of the intensity of the fighting, the Observatory said.
One security expert close to Damascus described low morale on the government side because hard-won territory had been lost.
The Shiite militant group did not specify which of Badreddine's many enemies it held responsible for his death.
Syrian government loyalists blamed Israel for the attack on Sunday.
The fighting, shelling and air strikes killed and wounded dozens of rebels
Hezbollah, backed by Iran, is a staunch ally of Assad in the four-year-long Syrian civil war.
The difficulty of making progress militarily will make a negotiated solution more attractive to the Kremlin.
The Syrian army had "withdrawn from a number of positions southwest of Aleppo and repositioned itself in new defensive lines".