The arrivals at the border began shortly after Syrian security forces opened fire on anti-government protesters across the country, killing 20 people, including two children aged 12 and 13, Syrian activists said.
The Local Coordination Committees, a group that tracks the anti-government protests in Syria, said most of the deaths occurred in the Barzeh neighborhood of the capital Damascus, as well as the suburb of al-Kaswa.
Several others died when security forces opened fire in the central city of Homs, sending residents fleeing into neighboring Lebanon.
The Syrian opposition says some 1,400 people have been killed as the government has cracked down on a movement demanding an end to four decades of Assad family rule - a popular uprising renewed each Friday after weekly Muslim prayers.
The violence has prompted thousands of Syrians to seek a safe haven in neighboring countries. Up to 1,000 Syrians crossed overnight into Lebanon through the al-Qusair crossing in the region of Akkar near Wadi Khaled in northern Lebanon, a Lebanese security official said.
There were at least six Syrians with gunshot wounds among those who crossed into Lebanon, the official said on condition of anonymity in line with military regulations. The wounded are receiving treatment in Akkar hospitals.