They were captured during the most serious cross-border attack since Syria's conflict began more than three years ago.
The video showed nine bearded men, eight of them in police uniforms and one wearing military fatigues.
The captives said they will be killed if Lebanon's militant Hezbollah movement, which backs Syrian President Bashar Assad, does not withdraw its fighters from Syria.
The al-Qaida-branch is also demanding the release of detainees held in Lebanon, some of whom were charged in connection to bombings that killed and wounded dozens of people over the past year, according to Lebanese media.
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Lebanese army commander Jean Kahwaji told An-Nahar newspaper that 20 soldiers remain missing. He defended his command decisions from criticism by local media, saying the soldiers' posts in border areas had been reinforced before the attack.
Other soldiers and policemen are believed to be held by other rebel groups who took part in the August 2 attack on the Lebanese border town of Arsal, which is home to tens of thousands of Syrian refugees.
The video, released by Nusra Front's media arm, al-Manara al-Baydha, appeared genuine and corresponded to other AP reporting of the events.
Hezbollah, which openly joined the war in Syria last year, is not likely to respond to the pleas of the captured troops, who appear to be speaking under duress.
Hezbollah leader Hassan Nasrallah has vowed to keep his fighters in Syria as long as needed, portraying the war as a struggle against Sunni extremists who pose a threat to Lebanon as well.
Meanwhile in Syria, attacks by Muslim extremists against an army air base in the country's north failed to break through fortifications, activists and state media said.
The Britain-based Syrian Observatory for Human Rights said the army crushed the latest offensive on the base that began last night with a suicide truck bomb. The Observatory's chief, Rami Abdurrahman, said that since the attacks on the base began early Wednesday, nearly 100 Islamic State fighters were killed and over 350 wounded.
The UN says more than 191,000 people have been killed since Syria's crisis began in March 2011.