The threat was made in a video AFP obtained from a Salafist cleric, Wissam al-Masri, who is mediating the release of 25 police and soldiers held by IS and the Syrian branch of Al-Qaeda, the Al-Nusra Front.
Four hostages have already been executed.
The video, filmed in a field with hills in the background, shows three men in blue uniforms, each kneeling in front of a fighter holding a knife to his throat.
The unidentified speaker, was wearing a hood and his companions’ faces were uncovered. From his speech, it was not possible to determine if he was from Lebanon, where French is widely spoken, or a third country.
Thousands of fighters from France and countries in North Africa where French is spoken have flocked to IS ranks.
The speaker attacked the politicians for what he said is their support for Lebanese Shiite movement Hezbollah, whose fighters are aiding Syrian President Bashar Assad in the civil war against largely Sunni Muslim rebels that include IS.
“To the allies of France in Lebanon — Hariri, Geagea and Jumblatt — the Islamic State is at war with Hezbollah, which is meddling in the affairs of Muslims in Shams (Syria) and has killed our women and our children,” he says.
He was referring to Sunni former prime minister Saad Hariri, right-wing Christian leader Samir Geagea and Walid Jumblatt, chief of the Druze community in Lebanon.
“You are certainly criminals, but you have added to your crimes today by your collaboration with Hezbollah and your transformation of the Lebanese army into a mere puppet in the hands of Hezbollah, with which it oppresses Sunnis.”
IS is a radical Sunni organisation that considers Shiite Muslims to be heretics. It has murdered many of them in a campaign of atrocities in areas under its control in Syria and neighbouring Iraq.
“You are therefore responsible for the fate of your fellow citizens. Their future, their life and death, depends on your next decision,” he said without making any specific demands of the three men.
However, the jihadists have demanded that Islamist prisoners held in Lebanese jails be released in exchange for the hostages.
Masri told AFP that he had met with IS leaders Thursday in Qalamoun, Syria, near the Lebanese border and seen nine of the soldiers.
“Two of them are in a very fragile state of health,” he said.
Lebanon has tried to insulate itself from the effects of the war in neighbouring Syria, but has been wracked by increasing instability and spillover from the nearly four-year conflict.
Last week, Lebanese Prime Minister Tammam Salam said 16 police and soldiers were still being held by Al-Nusra, and nine by IS.
“We have tried to negotiate with them… but things are very difficult.” -AFP