Syrian President Bashar al-Assad\'s troops pressed a fierce three-day assault against rebels in the central city of Homs on Monday but failed to make any new advances, activists said. Fighting between rebels and regime loyalists raged on the edges of insurgent-held districts, said the Syrian Observatory for Human Rights. The group also said that members of Lebanon\'s Hezbollah were fighting alongside government forces on one of the city\'s main fronts. \"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 the army was shelling the Khaldiyeh and Old City districts which have been under tight 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 population -- are Sunni Muslims, while Assad\'s clan belongs to the Alawite community. Although Lebanon is officially neutral in Syria\'s conflict, Hezbollah backed Assad\'s army in a recent battle for the key town of Qusair near Homs. 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. Asked about civilians in the city, Yazan said they \"have been living in shelters for months\" because of the shelling. Dubbed the \"capital of the revolution\" by activists, Homs is important because it is on the road linking Damascus to the coast. Its central location is also key as a supply route. Elsewhere, the army kept up its shelling of rebel areas in and near Damascus as it tried to secure the capital, said the Observatory. Among the military\'s targets were Yarmuk Palestinian refugee camp in southern Damascus and Qaboon in the east, as well as rebel bastion Daraya southwest of the capital. More than 100,000 people have been killed in Syria\'s war since March 2011, the Observatory estimates.