"This battle is ours... and I promise you victory," he said in a TV address.
Syrian rebels in the besieged town of Qusair say they are under heavy bombardment from Hezbollah combatants.
The town is close to the Lebanese border, a conduit for both the government and rebels to get weapons.
In the speech from an undisclosed location, Mr Hasrallah said if Sunni Islamists took over in Syria, they would pose a threat to the entire Lebanese population - Shia and Sunni Muslims, as well as Christians.
He said his movement could never be aligned with Syrian rebels who, in his view, were supported by the United States and Israel.
Hezbollah plunges deep into Syria conflict
Dozens of Hezbollah militants are said to have been killed fighting alongside Syrian troops in Qusair since 19 May, when government forces launched an offensive to recapture the rebel-held town.
Last week, US Secretary of State John Kerry said thousands of Hezbollah fighters were contributing significantly to the violence in Syria.
He added that Iran was actively supporting Hezbollah's involvement - a claim denied by Tehran.
Iran and Hezbollah are predominantly Shia, while Mr Assad's Alawite sect is an offshoot of Shia Islam.
The week-long fighting in Qusair intensified early on Saturday, when activists reported heavy bombardments, including two ground-to-ground missiles and an air strike as well as artillery and rocket fire.
Syrian state media said the army had launched a three-pronged offensive in the north, centre and south of Qusair, and was making big advances after "killing large numbers" of fighters.
Qusair is important for the Syrian government because it links the capital, Damascus, with the Alawite heartland on the Mediterranean coast. However, official media made no mention of the part played by Hezbollah.
The Lebanese group is also known to have lost a number of fighters in Qusair, prompting Lebanese President Michel Suleiman to warn the Shia militia against getting "bogged down in the sands of discord".
The Syrian Observatory for Human Rights, a UK-based activist group that monitors the conflict, said at least 22 people including 18 rebels had been killed in the latest fighting in Qusair. Dozens had been wounded, it added.
The leader of the Lebanese Shia militant Hezbollah movement, Hassan Nasrallah, has promised his supporters they will prevail in Syria, where they are backing President Bashar al-Assad.