Government forces pounded rebel positions in Homs with air strikes and artillery shells for a third day, AFP reported.
Opposition-aligned watchdog the Syrian Observatory for Human Rights reported that a woman and two children were killed in an air strike on the Old City of Homs on Sunday . Attacks resumed on Monday.
"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."
The group also reported that the Lebanese militia Hezbollah was present and fighting in areas of Homs.
"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 on Monday.
"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 is strategically important due to its central location and reputation as the 'centre of the revolution.'
At least 93,000 people have died since the Syrian uprising began in March 2011  according to the latest UN report, although the opposition-aligned Observatory reported last week that 100,000 have died during the 27 month conflict.