The Lebanese army, meanwhile, said gunmen kidnapped a soldier from his home in the port city, the second seized in northern Lebanon since Saturday.
Al-Nusra Front, which has previously executed one captive Lebanese soldier, issued its threat after troops cleared militants from Tripoli's historic bazaar district Saturday in an operation that left one civilian and a militant dead.
Many of the militants managed to withdraw to the Bab al-Tebbaneh district of the city, a Sunni Islamist stronghold, where troops were engaged in heavy fighting on Sunday, an AFP correspondent reported.
The army's offensive against the militants in Wednesday - who are suspected of having links to Al-Nusra and ISIS - sparked attacks on troops across the Tripoli region that left six dead.
The Al-Qaeda affiliate initially threatened to start executing its prisoners from 0800 GMT but then issued a second statement extending the deadline to 1200 GMT.In response Lebanon army declare in a statement “Operations will continue until we eliminate the last militant, news of efforts for evacuating militants are untrue”, Lebanon National News Agency reports.
Al-Nusra and rival terrorists of the ISIS group captured some 30 Lebanese soldiers and police in fighting around the eastern town of Arsal, close to the Syrian border, in August. IS has since executed two of its captives.
Islamist gunmen in Tripoli have carried out repeated attacks against the army and Shiites citizens.The August fighting in Arsal - a Sunni enclave within the mainly Shiite Bekaa Valley border region - was the most serious in Lebanon since the Syrian conflict erupted in March 2011.
The army said of warrant officer Fayez al-Ammuri was abducted by gunmen who stormed his home in Bab al-Tebbaneh on Sunday morning. Ammuri is the second soldier kidnapped by gunmen at the weekend, after a comrade was captured on a highway outside Tripoli on Saturday evening.
The army said it foiled an attempt by unidentified gunmen late on Saturday to abduct five of its soldiers in the Akkar region of northern Lebanon.
According to NNA, 4 soldiers have been killed in renewed clashes with gunmen in Bhanneen. Clashes renews on Sunday in Bhannin between the Lebanese Army and the militants after two military vehicles came under fire.
Also Lebanese Army announced in a statement Sunday the death of 4 soldiers, including 2 officers, in an ambush by a terrorist group in Dhour Mohamara of Minnieh in the afternoon.
The number of soldiers hospitalized at Halba Medical Center, has risen to 9 due to the ongoing armed clashes between troops and gunmen in Bhanneen, One additional soldier received first aid at Nahr el-Bared refugee camp before being transferred to Beirut for treatment, same reporters added.
The Lebanese Armed Forces raided on Sunday residential apartments in the region of Rass Sarj in Arsal and apprehended five Syrian nationals.