"The army launched an offensive several days ago on the neighbourhood of Deir Baalbeh with heavy bombing, and the fighting and attacks continued until the rebels withdrew," said the Syrian Observatory for Human Rights.
The Britain-based watchdog, which relies on a large network of activists and medics on the ground, said that several other rebel districts, long under siege by the army, were still holding the troops at bay.
It said that the fighting had triggered a humanitarian crisis in the city, referred to by anti-regime activists as "the capital of the revolution."
Homs, a longtime industrial heartland, was the target of a major army offensive in February that left 700 people killed, the majority civilians.
West of the city, the army also battered the rebel-controlled area around the Crac des Chevaliers crusader castle, a UNESCO-listed world heritage site.
In the northwest province of Idlib, clashes erupted for the fourth consecutive day between troops and rebels, mostly jihadist fighters, around Wadi Deif, the last military base under regime control in the area, the Observatory said.
Fighting also raged around Menagh military airport near Syria's second city of Aleppo, after rebels managed to penetrate the base on Thursday following a months-long siege, said the Observatory.
Assad's forces shelled farmland between Halab al-Jadida district and Mansura on the eastern outskirts of Aleppo, as warplanes overflew several towns in the north of the province.
Battles also erupted near an oil refinery in the northeast province of Raqa, where two rebels were killed, according to the watchdog.
Another two insurgents died in fighting in the eastern province of Deir Ezzor, which saw fierce battles in its provincial capital as fighter jets were sighted overhead.
Warplanes also launched raids on Kernaz in the central province of Hama, causing widespread destruction in the town, the Observatory said.
The Syrian Revolution General Commission (SRGC), a network of activists on the ground, said that the air strikes caused five homes to collapse on their inhabitants, leaving dozens of people injured.
Air strikes and artillery fire was also reported in several locations near Damascus, including Daraya to the southwest which the army has been trying to retake for several weeks, the Observatory said.
The SRGC reported clashes between the rebel Free Syrian Army and loyalist troops in the northeastern outskirts of the capital, while the army was targeting rebel strongholds in the Eastern Ghuta region with heavy mortar fire.
The Observatory said that 170 people -- 51 civilians, 62 rebels and 57 soldiers -- were killed on Friday in violence across Syria, where a pro-democracy uprising that erupted in March 2011 morphed into an armed insurgency after a bloody crackdown.
The watchdog puts the overall death toll from the conflict at more than 45,000.