The fighting in Tripoli started shortly before midnight Friday and intensified Saturday, the officials said on condition of anonymity in line with regulations.
Lebanon and Syria share a complex web of political and sectarian ties and rivalries, which are easily enflamed. Clashes in Tripoli last month killed at least eight people.
The conflict pits Sunni Muslims who support Syrian rebels trying to oust President Bashar al-Assad against members of the Alawite sect, an offshoot of Shiite Islam of which Assad is a member.
Smoke was seen billowing from several apartments near the city's Syria Street, the dividing line between the mainly Sunni Bab Tabbaneh neighborhood and the adjacent, Alawite-majority Jabal Mohsen. The area around Syria Street was mostly empty and gunmen were roaming the streets.
"We are being targeted because we support the Syrian people," a Sunni gunman told Associated Press Television. "We are with you [Syrian people] and will not abandon you."
In Syria, activists said government troops fired shells at Houla, a cluster of farming villages in Homs province where the U.N. says at least 108 civilians were killed May 25. The opposition and the government have each blamed the other for the massacre.
In Qatar, the head of Syria's largest exile opposition group said Saturday that he would welcome Arab military action aimed at brining a halt to attacks by Assad's regime against Syrian rebel forces and civilians.
Burhan Ghalioun, the leader of the Syrian National Council, made the comments before a meeting of Arab League foreign ministers, who discussed the bloodshed in Syria, including the Houla massacre.
Gulf nations such as Saudi Arabia and Qatar have pledged funds to aid Syria's rebels, but there is no direct evidence that the money is reaching anti-Assad forces or that the rebels are becoming better armed. The Arab League, however, does not appear ready to deploy its own troops.
After the meeting, the ministers issued a statement calling on the Arab world's two main satellite operators, Saudi Arabia-hosted Arabsat and Egypt's Nilesat, to suspend the broadcasting of Syria's state-run and private television stations.
The move, which would block the regime's ability to push its version of the uprising, is seen as another step by the Arab League to pressure Damascus, which was suspended from the 22-member bloc last year.
Syrian state TV quickly responded, saying the move is "part of the aggression against Syria and aims to silence the voice of its people." It added that the decision aims to "conceal the facts of what is going on in Syria."
With violence continuing despite nearly 300-strong U.N. observers on the ground in Syria, League chief Nabil Elaraby suggested that the monitors' mission shift into a peacekeeping one. "What is needed today is not only observing and investigating but supervising that the violence stops," Elaraby told the meeting.