The body of an unidentified Sunni man who had been shot dead was found on a road in the Bekaa Valley region bordering Syria in a suspected act of revenge for the policeman's murder while gunmen abducted an unknown number of Sunni residents from the area, security sources said.
Angry residents were blocking roads and set fire to tyres in the village of Bazzalieh, an AFP correspondent at the scene said.
The village is not far from the border town of Arsal where a former wife and young daughter of Abu Bakr al-Baghdadi, the head of the terrorist ISIS group that has seized parts of Syria and Iraq, were detained this week.
The flare-up came after Al-Nusra posted a photograph that it said showed the execution of detained Lebanese policeman Ali al-Bazaal, in a statement on its Twitter account picked up by the SITE terrorism watchdog.
Bazaal was one of around 30 Lebanese soldiers and policemen abducted by terrorists in August during fighting in Arsal.
"If the sisters that were unjustly arrested are not released, then after a short period of time the death sentence will be executed against another prisoner we hold," Al-Nusra said.
Lebanese security sources said they were trying to verify the claim.
On Wednesday, Lebanon's interior minister said authorities there were holding the daughter and former wife of IS chief Baghdadi.
Yesterday An ISIS commander has claimed that his wife and not that of the group leader Abu Bakr al-Baghdadi has been arrested by Lebanese authorities, and threatened to carry out retaliatory attacks.
Anas Sharkas, also known by his nom de guerre of Abu Ali Shishani, vowed to kidnap Lebanese women and children if his own wife and children are not released soon, in a video posted online.
While both the ISIS group and Al-Nusra are based in neighbouring Syria, they have clashed with Lebanese border forces and with the Hezbollah.
Last month a roadside bomb wounded three Lebanese soldiers near Arsal, where in August troops fought a fierce gun battle with terrorists who streamed across the border.
Fighting ended with a truce mediated by clerics, but the terrorists took with them the Lebanese army and police hostages.
At least four have since been executed and Qatari-led efforts to free the rest have so far failed.