Fighting between rebels and regime loyalists raged on the edges of insurgent-held districts, the Syrian Observatory for Human Rights said.
Hezbollah fighters from neighbouring Lebanon were fighting alongside government forces on one of the city's main fronts, it added.
"The shelling of Homs rebel areas continues, and it is fierce," Observatory director Rami Abdel Rahman told AFP.
"But the army has made no advances. They haven't been able to take any new areas back."
"Clashes raged on the edges of the districts. The army and (pro-regime militia) National Defence Force lost 32 men in two days," Abdel Rahman said.
"We can confirm now that Hezbollah is taking part in the fighting on the Khaldiyeh front, and that they are using the (majority Alawite neighbourhood of) Zahraa as a rear base," he added.
Homs city is home to a patchwork of religious communities. Most of Syria's rebels -- like the majority of the population -- are Sunni Muslims, while Assad's clan belongs to the Alawite minority.
"They have made no new advances at all... Still the shelling is continuous," Homs city-based activist Yazan told AFP via the Internet.
Asked about civilians in the city, Yazan said they "have been living in shelters for months" because of the shelling.
In Hama province, further north, the Observatory said four members of the National Defence Forces were killed in an explosion in Saboura.
Syria's state SANA news agency said the blast killed three civilians and wounded 18, including women and children.
The news agency said the blast was a suicide car bombing involving two bombers.
More than 100,000 people have been killed in Syria since the uprising against Assad's rule broke out in March 2011, the watchdog estimates.
Yesterday alone, at least 84 people were killed nationwide, 22 of them civilians.
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