About 20,000 Syrians have travelled across the main border crossing into Lebanon over the past 24 hours, a Lebanese security source working at the border said, after heavy fighting tore through several districts of Damascus, Reuters reported.

The number of Syrians who travel through the official Masnaa border crossing usually hovers around 5,000 per day, the source said.

Days of fighting in Damascus escalated sharply on Thursday, a day after a bomb attack which killed President Bashar al-Assad's brother-in-law, defense minister and a top general.

Some districts suffered heavy shelling and residents told Reuters many people had moved to quieter neighborhoods or were attempting to leave the country.

The Lebanese security source said foreigners including diplomats and some international aid workers were among those who crossed the border on Friday.

Assad's forces responded to pro-democracy demonstrations in March 2011 with bullets and arrests. The uprising has since become an armed revolt and rebels and government troops are battling around the country.