They came in buses and cars piled high with belongings, according to one eye-witness at the border yesterday.
A Lebanese security source said the refugees from the Yarmouk camp in Damascus had tried to flee on Sunday but the road was blocked by fighting.
Opposition activists said Syrian fighter jets bombed Yarmouk on Sunday, killing at least 25 people sheltering in a mosque. They added troops and tanks gathered outside the camp yesterday, and clashes inside continued.
Syria, which hosts half-a-million Palestinian refugees – most of whom live in Yarmouk and are descendants of those admitted after the creation of Israel in 1948 – has always cast itself as a champion of the Palestinian struggle, sponsoring several guerrilla factions.
Both Mr Assad's government and the mainly Sunni Muslim Syrian rebels have enlisted and armed Palestinians as the uprising has developed into a civil war.
The Yarmouk camp, on the southern fringes of Damascus, falls within a swathe of outlying suburbs running from the east to south-west of the capital from which rebels have been trying to push into the city centre and end 42 years of Assad family rule.