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.
The Local Co-ordination Committee, which tracks the anti-government protests, said most of the deaths happened in the Barzeh neighbourhood of the capital, Damascus, and the suburb of al-Kaswa.
Several others died when security forces opened fire in the central city of Homs, sending residents fleeing into neighbouring Lebanon.
The Syrian opposition said some 1,400 people have been killed in the government's crackdown 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 neighbouring countries.
Up to 1,000 Syrians entered Lebanon overnight through the al-Qusair crossing in the region of Akkar near Wadi Khaled in northern Lebanon, a Lebanese security official said. They included at least six people with gunshot wounds, he added.
The injured are receiving treatment in Akkar hospitals.
The new arrivals join thousands of other Syrians who fled to Lebanon in May and early June, most of them during the Syrian military's crackdown on the border town of Talkalakh, a few minutes walk from Lebanon's Wadi Khaled.
The military's recent sweep through north-western Syria, where armed resistance flared in early June, has also sent more than 11,700 refugees fleeing across the border, most to refugee camps in Turkey.
Defying government guns, thousands of Syrian protesters poured down city streets yesterday to press demands for President Bashar al-Assad to quit.
Syria's streets have become the stage for a test of endurance between a three-month-old pro-democracy movement, bloodied but resilient, and an iron-fisted but embattled regime. The latest round of protests and killings came as international pressure mounted on British-educated Assad.
"We will not stand by while the Syrian regime uses violent repression to silence its own people," Foreign Secretary William Hague said after the European Union expanded sanctions - asset freezes and travel bans - to more members of the Syrian leadership.
On Friday, security forces opened fire killing at least 15 people in Zabadani, a suburb of Damascus, including two children.
Five people were also killed by security forces' gunfire on Friday in Barzeh, a Damascus district three miles from the city centre.
But Syrian state television offered another version, saying gunmen, otherwise unidentified, had opened fire on security personnel and civilians, killing three civilians and wounding several security force members.
Five other fatalities occurred in al-Kasweh, a suburb of the capital; four in the central city of Homs, and one in Hama, also in central Syria.