Syrian President Bashar al-Assad's troops pressed a fierce three-day assault against rebels in the central city of Homs, but failed make headway, a watchdog and activists said.
Further north, in Hama province, an explosion killed four regime soldiers, while a car bomb went off in the capital Damascus, the Syrian Observatory for Human Rights said.
In Homs, fighting between rebels and regime loyalists raged on the edges of insurgent-held districts, the Observatory 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."
His Britain-based watchdog reported on Monday that the army was shelling the Khaldiyeh and Old City districts, under army siege for more than a year.
"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. Assad's clan belongs to the Alawite minority.
An activist on the ground said the military was trying to storm Homs on four fronts.
"They have made no new advances at all... Still the shelling is continuous," Homs city-based activist Yazan told AFP via the Internet.
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Civilians "have been living in shelters for months" because of the shelling, he said.
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.
The Observatory, reporting on the blast in Damascus, said: "A large explosion, apparently caused by an explosive device placed inside a car, rocked the district of Kfar Sousa."
A video posted to the website YouTube by activists late Monday night purportedly showed members of the Liwa al-Sham rebel group claiming responsibility for the blast.
Two members of the group said its fighters "on the ground targeted a group of senior officers responsible for crimes of the Assad regime."
They said a statement with the names of those targeted would be released later.
The southwestern neighbourhood of Kfar Sousa is home to a number of government and military intelligence buildings and has been targeted in previous attacks.
The army has kept up its shelling of rebel areas in around near Damascus as it tried to secure the capital, the Observatory said.
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.
On Sunday alone, at least 84 people were killed nationwide, 22 of them civilians.