The Lebanese army fanned out in the city of Tripoli in an attempt to calm the fighting, with soldiers patrolling the streets in armored personnel carriers and manning checkpoints. Authorities closed major roads because of sniper fire.
The fighting comes at a time of deep uncertainty in Syria, with rebels fighting government troops near Assad's seat of power in Damascus.
In Brussels, U.S. Secretary of State Hillary Rodham Clinton reiterated concerns that "an increasingly desperate Assad regime might turn to chemical weapons" or lose control of them to militant groups.
She also said NATO's decision on Tuesday to send Patriot missiles to Turkey's southern border with Syria sends a message that Ankara is backed by its allies. The missiles are intended only for defensive purposes, she said.
Turkish Foreign Minister Ahmet Davutoglu was quoted Wednesday in the Turkish newspaper Sabah as saying that Syria has about 700 missiles, some of them long-range.
"At this very moment we know where those missiles are, how they are being stored, whose hands they are in," he said.
U.N. Secretary-General Ban Ki-moon on Wednesday also urged Syria's regime against using its stockpile of chemical weapons, warning of "huge consequences" if Assad resorts to such weapons of mass destruction.
Syria has been careful not to confirm that it has chemical weapons, but the regime insists it would never use them against the Syrian people.
Ban also suggested that he would not favor an asylum deal for the Syrian leader as a way to end the country's civil war and cautioned that the United Nations doesn't allow anyone "impunity." Assad has vowed to "live and die" in Syria, but as the violence grinds on there is speculation that he might seek asylum.
Also Wednesday, U.S. officials said the Obama administration is preparing to designate a Syrian rebel group with alleged ties to al-Qaida as a foreign terrorist organization. The step seeks to isolate extremists within the Syrian opposition while the West tries to bolster those it supports.
The largely symbolic move will freeze any assets that members of the group, Jabhat al-Nusra, have in U.S. jurisdictions and bar Americans from providing the group with material support, the officials said.
The administration hopes the designation will complement its expected announcement to recognize the opposition's new leadership council as the sole legitimate representative of the Syrian people at an international conference in Morocco on Dec. 12.
The officials spoke on condition of anonymity because they were not authorized to preview the designation publicly.
The Syrian crisis has spilled over into Turkey, Israel and Jordan over the past 20 months, but Lebanon is particularly vulnerable to getting sucked into the conflict. The countries share a complex web of political and sectarian ties and rivalries that are easily enflamed. Lebanon, a country plagued by decades of strife, has been on edge since the uprising in Syria began, and deadly clashes between pro- and anti-Assad Lebanese groups have erupted more than a dozen times.
Tensions in Tripoli have been mounting since last week, when reports emerged that some 17 Lebanese Sunni fighters were killed inside Syria, apparently after they joined the rebellion against Assad. The bodies of some of the men were later shown on Syrian state TV.
On Wednesday, Syrian Ambassador Ali Abdul Karim Ali told Lebanese Foreign Minister Adnan Mansour that Damascus has agreed to repatriate the men's bodies. Lebanon's National News Agency said the countries would soon discuss how to hand over the bodies.
Anti-Syrian politicians in Lebanon have criticized the government, which is led by the Shiite Hezbollah group, for what they call a lack of effort to get the bodies back. Hezbollah supports Assad, whose regime is dominated by the president's Alawite sect - an offshoot of Shiite Islam.
The fighting in Tripoli pits the Sunni neighborhood of Bab Tabbaneh, which supports Syria's predominantly Sunni rebels, against the adjacent Alawite neighborhood of Jabal Mohsen, which supports Assad.
The sounds of gunfire and explosions echoed near the clashing neighborhoods, and police closed roads leading to the area. Nearby cars raced to dodge sniper fire.
Lebanese soldiers parked tanks on a bridge and in a roundabout near the area and patrolled in dozens of armored vehicles, but did not enter the neighborhoods themselves to try to stop the clashes.
Lebanese security officials said at least six people have been killed and more than 50 wounded in the Tripoli fighting since Tuesday. The officials spoke on condition of anonymity because they are not authorized to talk to the media.
Also Wednesday, a Syrian woman living in the Damascus district of Abu Rumaneh said that the home Jihad Makdissi, a Foreign Ministry spokesman and prominent defender of the regime, went up in flames on Tuesday.
"No firefighters came to put the fire out," she told The Associated Press by telephone, implying the house had been torched by regime supporters.
Speculation has been growing about Makdissi's relationship to the regime.
Lebanese security officials have said Makdissi flew Monday from Beirut to London, but it is not clear whether Makdissi defected, quit his post, or was forced out. The government has not commented on the matter.
In Washington, U.S. State Department spokesman Mark Toner told reporters the U.S. has heard he is in London.
"If true, this is obviously another sign of the regime crumbling from within as those closest to Assad are realizing that the end is nigh," he said.
Syria's uprising began with peaceful protests in March 2011 and later escalated into a civil war that the opposition says has killed more than 40,000 people.
Fighting continued around Syria on Wednesday, with rebels clashing with government troops around the capital, Damascus, and elsewhere.
Government forces shelled and flew fighter jets over a number of restive areas south, east and north of the capital, clashing with rebels in the eastern suburbs of Zamalka and Arbeen, according to the Britain-based Syrian Observatory for Human Rights. At least two rebel fighters were killed in clashes and three civilians killed in government shelling, the group said.
While fighting has intensified in the suburbs, rebels have not yet pushed major fighting into the city itself.
A Western diplomat, who monitors Syria from Jordan, said Assad is still in control of much of Damascus.
"It's true that rebel attacks in the capital are becoming more focused, organized and painful to Assad's regime," he said, speaking on condition of anonymity to avoid jeopardizing his information gathering. "He is still in control of his security and more or less all of the capital."
In the north, a Syrian jet bombed the rebel-held town of Tal Abyad, near the Turkish border, while rebels responded with anti-aircraft fire, Turkey's state-run Anadolu agency said. At least two wounded people were brought to the Turkish border town of Akcakale for treatment.
An activist video from the northern province of Idlib showed residents of the village of Talmanis digging through rubble in search of survivors after a government air strike. The video then shows bodies lying in the back of a pickup truck while an off camera voice says five people from the same family were killed in a rocket attack from a nearby army base that rebels have repeatedly attacked.
The videos appeared genuine and corresponded to other reports on the incidents. The Syrian government greatly restricts journalistic access to the country, making independent authentication of events nearly impossible.
Associated Press writers Karl Ritter in Doha, Qatar, Suzan Fraser in Ankara, Turkey, and Jamal Halaby in Amman, Jordan, contributed to this report.