Nasrallah said Saturday that Hezbollah had entered a phase in which it would fight on two fronts. He framed the conflict in Syria as a struggle against an extremist opposition backed by Israel and the United States and characterized Assad's regime as Hezbollah's "backbone."
"We will bear all responsibilities," he said of Hezbollah's involvement in Syria. Addressing his fighters, he added: "I have always promised you victory, and I promise victory again."
The fighting in Qusair has proved costly for Hezbollah, with scores of bodies transported back to Lebanon for burial over the last week.
Activists in the town said the bombardment Saturday morning was the heaviest yet, with as many as 30 shells falling every minute.
Ringed by Hezbollah militants and army forces, Qusair, just a few miles from the Lebanese border, has been the focus of an intense battle for six days. Gaining control of it is pivotal to government efforts to establish a grip on central Syria.
Activists linked the intense push on Saturday to Nasrallah's speech, the first since the offensive began.
"We were expecting a more decisive attempt to advance before Nasrallah's speech, and it has happened," said Sami al-Rifaie, an activist based in Qusair. "He wants to appear in front of his people victorious."
Rifaie said shelling started around 6:30 a.m. and continued until noon. Two surface-to-surface missiles also fell on the town, he said.
"I just went back to my house to check on my brother, and on my way home I saw one had hit very close to my house," he said. "I'm lost for words. I haven't seen anything like this before. It's a residential area, and there was destruction for a radius of 100 to 200 meters."
Rifaie said Hezbollah militants had tried to take control of the al-Ghaida checkpoint on the southern side of the town Saturday but had been pushed back.
Since the push began on Qusair, fighting has flared in Lebanon's second city of Tripoli, where clashes between pro- and anti-Syrian government forces have claimed 25 lives over the last week.
Nasrallah condemned the violence in Tripoli, arguing that it would be better if the opposing factions crossed the border and fought in Syria.