Zeina Khodr, Al Jazeera's correspondent said from Tripoli: "This is the worst fighting I have witnessed, there is sporadic gunfire. The situation is very dangerous.
"One man was shot in the head in his car by sniper fire ... This is not an organised campaign of violence, but local friction."
The AFP news agency reported quoting security officials that four people were killed and at least 33 others injured in Sunday's clashes.
Fighting began at 4.15am local time (01:15 GMT) in Bab al-Tabbaneh and Jabal Mohsen, north of Tripoli.
Clashes extended to al-Qobbe zone in the city's east where families could be seen fleeing the fighting.
A Lebanese security official said pro-government Sunni fighters fought a group of Alawites, a dissident branch of Shia Islam which supports the Shia opposition group Hezbollah.
Bab al-Tebbaneh and al-Qobbe are mainly Sunni districts while residents of Jabal Mohsen are predominantly Alawite.
Calm was restored in the afternoon as representatives of the feuding parties, including Najib Mikati, a former prime minister, met in Tripoli and agreed on the Lebanese army taking charge of security and for fighters to keep off the streets, a participant said.
However, after sunset sporadic fighting in the area resumed, security officials said.
The violence took place amid stalled efforts by Fouad Siniora, the prime minister, to form a new government of national unity following a breakthrough deal last month to end a long-running crisis that had brought the country to the brink of civil war.
The deal, brokered in Doha, Qatar, led to the election of Michel Sleiman, the former army chief, as president.
The accord also called for the formation of a cabinet in which the opposition will have veto power over key decisions as well as a new electoral law.
"Despite the Doha agreement, political wrangling has been continuing," Khodr said.
"A lot of observers believe as long as there is no governmental structure, how do you expect reconciliation in the streets? Therefore, Lebanon's problems have not really been solved."
Muslim fighter killed
In a separate incident, a Muslim fighter was critically wounded on Sunday in a blast near the Palestinian refugee camp of Ain el-Helweh in south Lebanon which injured four others, a security official told the AFP new agency.
Imad Yassin, a senior member of the Jund al-Sham group, was wounded along with two of his bodyguards when a charge placed in a rubbish bin exploded in the Taameer Ain el-Helweh area outside the camp, the official said.
A woman and an eight-year-old girl were also slightly wounded in the blast which prompted several families to flee the area.
Tension was high inside the camp with fighters from the mainstream Palestinian Fatah faction deploying to prevent an escalation, an AFP correspondent reported.