The coastal city has seen repeated clashes between Sunni militants sympathetic to rebel fighters in neighbouring Syria and Alawites loyal to the Damascus regime.
The Sunnis have recently focussed their attacks on the army over its alleged support for Damascus ally Hezbollah.
The latest clashes erupted on Friday at the city's historic market, which is a major tourist attraction.
On Sunday army mortar fire pounded the impoverished, outlying neighbourhood of Islamist bastion Bab al-Tebbaneh, where the gunmen were pushed back and cornered.
Five civilians have been killed in three days, among them a child and two adults on Sunday, said a security official.
After pleas from residents and mediation by clerics, the army allowed thousands of civilians who had been caught in the crossfire for hours to flee Bab al-Tebbaneh.
The AFP journalist on the spot described chaotic scenes as people of all ages left their ravaged neighbourhood.
Many of the women walked out in their pyjamas, crying as they and the men were searched by army and intelligence troops.
Men carried out children and elderly people too weak to walk.
Five wounded civilians and dozens of people suffering from illness were evacuated in Red Cross ambulances.
Many went to stay with relatives. Others were put up in schools, which the authorities said would be closed on Monday, along with universities, because of the violence.
It is unclear how long the informal humanitarian truce will last, and the army has said it has no intention on letting up in the fight.
"We are going through with this operation to the end," a military source said.
Bab al-Tebbaneh is home to some 100,000 people, while the parts of the neighbourhood where the fighting is worst is usually inhabited by some 15,000.
The AFP journalist said that even in areas far from the fighting, the streets were empty, with people too fearful to leave their homes.
- Execution threat -
Earlier, the army said gunmen ambushed a patrol north of Tripoli, killing four soldiers.
"This afternoon, an army unit was targeted by a terrorist group while deploying in Duhur al-Mohammara. A clash broke out, which caused several casualties in the (militants') ranks, while four soldiers including two officers were martyred," said a statement.
Meanwhile a soldier kidnapped at the weekend was released after mediation by officials and clerics, a security source said.
A second soldier kidnapped on Sunday was still being held by the gunmen.
Al-Qaeda's Syrian affiliate meanwhile threatened to kill at dawn on Monday a Lebanese soldier it captured in August during a bloody battle in restive Arsal unless the army halts its Tripoli operations.
Al-Nusra Front has previously executed one captive Lebanese soldier.
The latest threat, issued via the group's Twitter account, came after two previous warnings on Sunday, which it apparently backtracked on.
Both Al-Nusra and rival Islamic State group jihadists captured 30 Lebanese soldiers and police in August around the eastern town of Arsal, close to the Syrian border.
They have since executed two of them.
Al-Nusra has previously demanded that in return for the release of its prisoners, Shiite militant group Hezbollah end its intervention in Syria on the side of President Bashar al-Assad's regime and that Lebanon free jailed Islamists.
The Lebanese government has so far rejected the terms.
Islamist gunmen in Tripoli have carried out repeated attacks against the army, accusing it of cooperating with Hezbollah.
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.
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The Sunnis have recently focussed their attacks on the army over its alleged support for Damascus ally Hezbollah.
The latest clashes erupted on Friday at the city's historic market, which is a major tourist attraction.
On Sunday army mortar fire pounded the impoverished, outlying neighbourhood of Islamist bastion Bab al-Tebbaneh, where the gunmen were pushed back and cornered.
Five civilians have been killed in three days, among them a child and two adults on Sunday, said a security official.
After pleas from residents and mediation by clerics, the army allowed thousands of civilians who had been caught in the crossfire for hours to flee Bab al-Tebbaneh.
The AFP journalist on the spot described chaotic scenes as people of all ages left their ravaged neighbourhood.
Many of the women walked out in their pyjamas, crying as they and the men were searched by army and intelligence troops.
Men carried out children and elderly people too weak to walk.
Five wounded civilians and dozens of people suffering from illness were evacuated in Red Cross ambulances.
Many went to stay with relatives. Others were put up in schools, which the authorities said would be closed on Monday, along with universities, because of the violence.
It is unclear how long the informal humanitarian truce will last, and the army has said it has no intention on letting up in the fight.
"We are going through with this operation to the end," a military source said.
Bab al-Tebbaneh is home to some 100,000 people, while the parts of the neighbourhood where the fighting is worst is usually inhabited by some 15,000.
The AFP journalist said that even in areas far from the fighting, the streets were empty, with people too fearful to leave their homes.
- Execution threat -
Earlier, the army said gunmen ambushed a patrol north of Tripoli, killing four soldiers.
"This afternoon, an army unit was targeted by a terrorist group while deploying in Duhur al-Mohammara. A clash broke out, which caused several casualties in the (militants') ranks, while four soldiers including two officers were martyred," said a statement.
Meanwhile a soldier kidnapped at the weekend was released after mediation by officials and clerics, a security source said.
A second soldier kidnapped on Sunday was still being held by the gunmen.
Al-Qaeda's Syrian affiliate meanwhile threatened to kill at dawn on Monday a Lebanese soldier it captured in August during a bloody battle in restive Arsal unless the army halts its Tripoli operations.
Al-Nusra Front has previously executed one captive Lebanese soldier.
The latest threat, issued via the group's Twitter account, came after two previous warnings on Sunday, which it apparently backtracked on.
Both Al-Nusra and rival Islamic State group jihadists captured 30 Lebanese soldiers and police in August around the eastern town of Arsal, close to the Syrian border.
They have since executed two of them.
Al-Nusra has previously demanded that in return for the release of its prisoners, Shiite militant group Hezbollah end its intervention in Syria on the side of President Bashar al-Assad's regime and that Lebanon free jailed Islamists.
The Lebanese government has so far rejected the terms.
Islamist gunmen in Tripoli have carried out repeated attacks against the army, accusing it of cooperating with Hezbollah.
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.
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